United are reportedly ready to sell the forward rather than risk losing him on a free next summer.
The Dutchman endured a difficult 2014/15 campaign under new boss Louis Van Gaal as a series of injuries limited his game time and severely hampered his form.
With United having struggled up front last season, it is thought that they will look to sign another forward in the summer transfer window. However, Van Persie, who only has a year left on his contract, is widely expected to leave Old Trafford along with several other players.
According to the Il Messaggero report, officials from both clubs have met in Berlin to thrash out an agreement, with a price of around €12-13 million being touted, which would work out at around £10.9 million for the Serie A side.
The 31-year-old has also reportedly been offered a four-year-contract at the club as they look to secure him ahead of a number of other suitors. The deal would represent a big loss on the fee United paid Arsenal for him back in 2012, but they are said to be keen on agreeing a deal now rather than risk losing him on a free transfer next summer.