Galliani also confirmed the midfielder had been "close" to joining the Rossoneri before moving to LA Galaxy from Real Madrid.

The former England captain is keen to keep up his match sharpness in order to remain part of the national squad but with the Major League Soccer season coming to a close he will need to find alternative arrangements.

Last year he joined up with Arsenal and there have been reports in Italy that Milan could be his next port of call.

Galliani confirmed that manager Carlo Ancelotti would have the final say but insisted the club would be happy to have the 33-year-old midfielder train with them.

"I have not heard from Beckham since the night before he transferred to Galaxy," said Galliani.

"He was close to (joining) Milan before going to California, but I don't know anything about the rumours in circulation. But if Beckham wanted to train with Milan, then I would have to ask coach Carlo Ancelotti, but from the club's point of view, there would not be any problem.

"But Beckham is another club's player who has a contract with that other club."

The former Manchester United and Real Madrid player is eager to stay in Fabio Capello's England plans as he bids to add to his 107-cap tally.

Two more caps would see him overtake Bobby Moore as the country's most capped outfield player.