The 29-year-old Ghanaian is thought to be available for a cut-price £3.9m this January, with new Milan boss Clarence Seedorf wanting to sell him before his contract expires in the summer.
Muntari worked with Bruce during a loan spell at Sunderland in 2011 and a source told the Daily Star that the sacking of Massimiliano Allegri at the San Siro has opened the door for a possible reunion.
"AC would ideally like to offload Muntari this month," the source is quoted as saying. "If they don't cash-in on him now, they will lose him for nothing when his contract runs out in the summer.
"He was close to Allegri and one of the former coach's key players in the team. But that is no longer the case, and it appears his days at the San Siro are numbered.
"Sulley would welcome a return to England and the chance to work with Steve Bruce again. Bruce took him on loan from Inter when he was in charge at Sunderland three years ago, and Muntari has a big respect for the Hull manager."
Muntari made nine appearances in his temporary spell at Sunderland and has also previously played in the Premier League for Portsmouth, for whom he scored five times in 33 games.