Michigan fired Hoke on Tuesday after the Wolverines finished 5-7 and failed to qualify for a bowl for the first time since 2009. During four seasons at Michigan, Hoke compiled a 31-20 record.
Carr, who won the 1997 National Championship and had a 122-40 record at Michigan, gave his vote to former Wolverines quarterback Harbaugh on Thursday.
"If it were my choice -- which it is not -- I like (Jim) Harbaugh," Carr said Thursday.
Harbaugh, who played at Michigan from 1983-1986, has been linked to his alma mater in recent months. He is in his fourth season with the 49ers and reached the NFC Championship Game in his first three seasons, including a Super Bowl appearance following the 2012 season. He had a 29-21 record in four seasons at Stanford.
The 49ers are 7-5 this season and there have been several reports that Harbaugh's time in San Francisco could be nearing an end. After a loss to the Seattle Seahawks on Thanksgiving, 49ers CEO Jed York apologized for the team's play, saying it "wasn't acceptable."
Harbaugh has one season remaining on his contract, and ESPN's Adam Schefter has reported that the Oakland Raiders and New York Jets want to acquire him in a trade.
- Paul Palladino