Mattis got the nod from Trump on Thursday, people close to the veteran told The Washington Post.
There is a hangup with the selection, however. The National Security Act of 1947 prohibits defense secretaries from having been in active military service within the previous seven years. Mattis retired in 2013. In order to take the position, then, Congress must pass legislation to bypass the restriction.
Such an exception is not unprecedented, though. Congress acted to allow Gen. George C. Marshall to serve as Pentagon chief in 1950, even though he was still in active Army service.
An official announcement is expected early next week, reports said.
If true, Mattis' appointment will leave just eight Cabinet leadership posts to be filled, including secretary of state.
The following is a list of appointments made so far and potential candidates for other vacancies:
Vice President: Mike Pence
Prior service: Governor of Indiana (2013-2017), U.S. House of Representatives (2001-2013)
Trump chose Pence to be his vice presidential running mate this summer, prior to the Republican National Convention.
The 50th governor of Indiana will serve as Trump's second-in-command and president of the Senate. He is also first in the presidential line of succession. A former attorney, Pence was a supporter of Indiana's controversial legislative efforts to pass a religious freedom bill.
Secretary of Defense: James N. Mattis
Prior service: U.S. Marine Corps (1969-2013), CENTCOM commander (2010-13), United States Joint Forces commander (2007-10)
Mattis is a 44-year Marine Corps. veteran who held several military leadership positions, including at U.S. Central Command and NATO. He fought in the first Persian Gulf War, as well as the operations in Afghanistan and Iraq.
He replaced Gen. David Petraeus in 2010 when he left the Pentagon to become CIA director.
Chief of Staff: Reince Priebus
Prior service: Republican National Committee chairman (2011-2017), Wisconsin Republican Party chairman (2007-2011)
Born in New Jersey, Priebus moved to Wisconsin at an early age and got involved in politics as a teenager. He became leader of the state's Republican party after an unsuccessful bid for state senate.
As party chief, he corroborated on issues with Gov. Scott Walker and House Speaker Paul Ryan. After his ascension to RNC chair, Priebus spearheaded efforts to unify the party and supported Trump through controversies during his campaign this year.
Attorney General: Jeff Sessions
Prior service: U.S. Senator from Alabama (1997-2017), Alabama attorney general (1995-1997)
Before entering politics, Sessions served in the U.S. Attorney's Office for 12 years. Before that, he was an attorney in private practice and was a captain in the U.S. Army for four years.
Sessions is considered by many as one of the most conservative lawmakers in the Senate. He supported many of President George W. Bush's policies, including the decision to invade Iraq in 2003.
National Security Advisor: Michael Flynn
Prior service: Defense Intelligence Agency director (2012-14), U.S. Army (1981-2014)
Flynn's appointment is unique in that he is the only Democrat Trump has named to his administration team so far.
He reached the rank of Lieutenant General in 33 years of Army service and earned many of the medals available to servicemen in the branch. Earlier this year, he was named as a possible running mate for Trump.
He retired from his post as President Barack Obama's Defense Intelligence Agency director in 2014, but some sources said he was forced out at the Pentagon due to his "chaotic" management style and clashes with other high-ranking Defense officials.
White House Chief Strategist: Steve Bannon
Prior service: Breitbart News (2012-2016), U.S. Navy (1976-83)
Bannon has been by far Trump's most controversial appointment to date. The former entertainment executive took over leadership of the right-leaning Breitbart News after the death of founder Andrew Breitbart in 2012, and helped grow the site to nearly 40 million unique visitors last month.
Some prominent Democrats, including Senate Minority Leader Harry Reid, have called for Trump to rescind the appointment of Bannon, saying Breitbart is an "alt-right" site and that Bannon is anti-Semitic, claims that Breitbart editors and others who know Bannon have vigorously refuted.
Director of Central Intelligence: Mike Pompeo
Prior service: U.S. House of Representatives (2011-2017), U.S. Army (1986-91)
Pompeo received a law degree from Harvard University before founding Thayer Aerospace and leading an oilfield equipment company.
Pompeo was elected to the House, representing Kansas, in 2010 and was a member of the House Select Committee on Intelligence.
Secretary of the Treasury: Steven Mnuchin
Prior service: Goldman Sachs, Hollywood film producer
Mnuchin was an early supporter of Trump's and fits in line with the president-elect's image as a Washington outsider. The Yale graduate brings a wealth of business experience to the Treasury role, though he has never served in government -- in stark contrast to the man currently in the post, Jack Lew.
He served as the Trump campaign's finance chair for the past six months.
Secretary of Commerce: Wilbur Ross, Jr.
Prior service: Financial investor
Like Mnuchin, Ross has never served in government but brings a vast cachet of finance experience. A billionaire, like the president-elect, Ross served for decades as an investor and knows business.
Also an early Trump supporter, Ross was also a longtime Democratic supporter and donor.
Health & Human Services Secretary: Tom Price
Prior experience: U.S. House (2005-2017), Georgia Senate (1997-2005)
One of the GOP's leading lawmakers out to dismantle the Affordable Care Act, Price was an orthopedic surgeon before he entered politics in the mid-1990s.
"The problem that I have with Obamacare is that its premise is that Washington knows best," he said earlier this year.
Secretary of Transportation: Elaine Chao
Prior service: Labor secretary (2001-09), deputy transportation secretary (1989-91)
Chao is a unique selection in Trump's cabinet because she is so far the only appointee who has served in a similar capacity before. She was George H. W. Bush's deputy transportation secretary for two years. A decade later, she became George W. Bush's labor secretary.
Secretary of Education: Betsy DeVos
Prior service: Chair of Michigan Republican Party (1996-2000, 2003-05)
DeVos has been a major proponent of the "school choice" voucher movement to enable American parents to choose which public or private school to send their children to. A billionaire like Trump, DeVos has also been one of the GOP's biggest donors in recent years.
DeVos said she is honored to help "make American education great again."
Ambassador to the United Nations: Nikki Haley
Prior service: Governor of South Carolina (2011-17), South Carolina House (2005-11)
One of the youngest members of Trump's top administration team, Haley took office in Charleston before she was 40. She was a semi-popular leader in South Carolina, particularly after barring the Confederate Flag from state grounds following last year's shooting at a historically black church.
Though honored to become the primary ambassador to the U.N., Haley said the decision to accept was "difficult because I love serving South Carolina more than anything,"
Other potential administration candidates:
Labor Secretary - Restaurant businessman Andy Puzder, former Labor executive Victoria Lipnic, Pennsylvania Rep. Lou Barletta.
Housing Secretary: Former GOP candidate Ben Carson, Center for Neighborhood Enterprise founder Robert Woodson, Missouri Rep. Blaine Luetkemeyer.
Veterans Affairs: Former Massachusetts Sen. Scott Brown, Hawaii Rep. Tusli Gabbard, former Alaska Gov. Sarah Palin.