According to Joe Pequeno of CBS5, Michigan's offer is for six years and $49 million.
Based on average yearly value, the contract would make Harbaugh the highest-paid coach in college football. Alabama's Nick Saban, the current highest-paid coach, earned $6.9 million this season as part of a new deal he signed in the spring.
Though he's been mentioned in connection to the Michigan opening since ex-coach Brady Hoke was fired earlier this month, Harbaugh hasn't spoken publicly about Michigan and reportedly left school officials with the impression he wants to stay in the NFL during a recent meeting.
ESPN's Adam Schefter reported Wednesday that while Harbaugh was previously thought to be unlikely to end up at Michigan, one source familiar with Harbaugh's thinking said the coach was now "considering" the school.
Harbaugh has one year remaining on his contract with the 49ers but isn't expected to return to the team due in part to a contentious relationship with management and ownership.
San Francisco is 7-7 this season and was eliminated from playoff contention after losing to the Seattle Seahawks last week.
Harbaugh, 50, played quarterback at Michigan from 1983-86 and spent part of his childhood in Ann Arbor while his father Jack was was an assistant under legendary former Wolverines coach Bo Schembechler.
The coach of the 49ers since 2011, Harbaugh took San Francisco to three straight NFC championship games, including an appearance in Super Bowl XLVII in 2013, before failing to make the playoffs this season.
Harbaugh served as head coach at Stanford before taking the 49ers job and led the Cardinal to an Orange Bowl victory in his final year in Palo Alto.
Michigan's next hire will be its third different head coach since Carr retired after the 2007 season.
- Ben Estes