Players had an opportunity to read the team's official statement on Tuesday before it was released to the public.
"Obviously we were a little shocked because no one really knew," Barkley said, via NJ.com. "We came together as a team, and coach (Pat Shurmur) kind of said he is in high spirits, he is getting better, he is going to fight this thing, and we are going to be there for him and pray for him."
"... He is part of the reason why I'm here, why I got drafted to the New York Giants. It (stinks) to hear that for someone you care about, but at the same time you know the type of person he is and it sounds like he is in very high spirits. He knows for sure that everyone on the team has his back. We're there for him. We're going to continue to love him and pray for him."
Gettleman has been high on the 6-foot, 233-pound Barkley prior to the team selecting the Penn State star with the second overall pick of the 2018 NFL Draft.
"He was touched by the hand of God, frankly," the 67-year-old Gettleman said of Barkley, who rushed 217 times for 1,271 yards and 18 touchdowns last season while also reeling in 54 passes for 632 yards and two scores.
"We felt Saquon was the best player in the draft. ... I haven't seen a guy like this in a long time."
Gettleman said in part of his lengthy statement on Tuesday that the prognosis is positive and that he is expected to start treatment in the "very near future."
Per the Mayo Clinic, lymphoma is a cancer of part of the body's germ-fighting network and more common in males over the age of 55.
"It was tough," wide receiver Sterling Shepard told multiple media outlets on Wednesday night at the David Tyree Charity Bowl to benefit Children of the City, a Brooklyn-based organization dedicated to improving the lives of impoverished kids.
"But (Gettleman) is a strong guy, just from what I know being around him these last few months. He'll beat it. We have faith in that. Coach told us that the doctors are very confident and he's confident, so that ultimately makes us confident."
Gettleman is entering his first year as general manager of the Giants after holding the same position from 2013-16 with the Carolina Panthers.
Should Gettleman need to focus squarely on his recovery, assistant general manager Kevin Abrams has been with the organization for 19 years. He was the interim GM after Jerry Reese was dismissed during the 2017 season.
Gettleman headed the pro personnel department with the Giants from 1998-2012 before taking the Panthers' GM job.
He was hired by the Giants to help turn around a team went 3-13 last season. Gettleman overhauled the roster this offseason with some notable acquisitions -- namely offensive tackle Nate Solder -- and cut several key veterans, including wide receiver Brandon Marshall and cornerback Dominique Rodgers-Cromartie.