The Italy international is claimed to have agreed personal terms with the Rossoneri, with the clubs locked in negotiations over a transfer fee.
According to reports in Italy, Juve are demanding €40million for the 30-year-old, although there is some speculation a part-exchange deal involving either Mattia De Sciglio or Alessio Romagnoli could be agreed.
Bonucci's agent, Alessandro Luci, has refused to deny talks are taking place but offered no indication of whether the move will go through.
"There are no feelings at the moment," he said, as quoted by Calciomercato.com. "We just have to wait."
The transfer would represent a stunning piece of business from Milan, who have already invested heavily in their playing squad as they seek to build a team capable of returning to the Champions League.
Bonucci was linked with Manchester City and Chelsea last season and his future in Turin was cast into doubt after a row with head coach Massimiliano Allegri on the touchlines during a Serie A match with Palermo in February.
He was dropped from the squad for their next game against Porto in the Champions League but the duo later held clear-the-air talks and he was brought back into the first team.
Bonucci posted on his official Instagram page on Thursday, writing "Let's get back to work. Ready to start again!" alongside a picture captioned with text in Juventus colours.