MMQB.com's Albert Breer told Fox Sports Radio's Colin Cowherd that a Harbaugh return could be in the works.
"By the way, Albert Breer on the way out said that Jim Harbaugh to the Rams rumor is a very real thing," Cowherd said following his interview with Breer, via CBSSports.com.
Harbaugh, currently the coach at Michigan, spent four seasons coaching the San Francisco 49ers from 2011-2014.
Under Harbaugh, San Francisco was 44-19-1 and made three straight appearances in the NFC Championship Game. In 2012, the 49ers advanced to Super Bowl XLVII before losing to the Baltimore Ravens, who were coached by Jim's brother, John.
Harbaugh owns a 78-32 record as a college coach at San Diego, Stanford and Michigan. The sixth-ranked Wolverines (10-2) face 11th-ranked Florida State in the Orange Bowl on Dec. 30.
The Rams fired coach Jeff Fisher on Monday after a 4-9 start. Los Angeles announced a two-year contract extension through 2018 for Fisher on Dec. 4.
John Fassel, the son of former longtime NFL coach Jim Fassel, was named the Rams' interim coach.