Shanahan likely will get the job, barring "unforeseen glitches," the Post's "Redskins Insider" column said Monday, referring to "sources in the organization."
Earlier in the day, the Redskins announced the firing of Jim Zorn, who had coached the team for two years.
Shanahan, who coached the Broncos from 1995 until he was fired at the end of the 2008 season, was in Washington Monday. He would be the sixth full-time Redskins head coach since Daniel Snyder bought the team in 1999.
The Broncos won the Super Bowl under Shanahan in 1997 and 1998.
The firing of Zorn came after the team returned to the Washington area from a season-ending 23-20 loss at San Diego. The Redskins were 4-12 this season.
Bruce Allen, hired Dec. 17 as general manager, said in a statement his study of the team in the past three weeks indicated a change was needed.
"The status quo is not acceptable," Allen said in a release. "I felt it was necessary to not waste a moment of time building this team into a winner."