According to Rossoneri vice-president Adriano Galliani, the Premier League club have made contact over a possible move but are yet to lodge a formal offer.

Gattuso has not been playing regularly at the San Siro this season and he admitted last month that he might have to consider his options in January.

Milan have always insisted he will not be going anywhere and on Thursday they offered him a new deal to stay with the club for the rest of his career.

Reports in the Italian media suggest Gattuso has rejected the chance to extend his contract but Galliani is adamant that he will at least honour the terms of his existing agreement.

Galliani has nevertheless admitted that Manchester City are monitoring the 31-year-old's situation.

Chelsea had also been linked with Gattuso but Carlo Ancelotti has already dismissed speculation that he might try to bring in a player he worked with during his time in charge at Milan.

"There is a proposal by Manchester City although at present there's still no kind of agreement or something written," Galliani told the Italian press.

"But Chelsea are not interested in a purchase. I've talked with Ancelotti."

Galliani added: "Milan is not a hotel where you can check out anytime you want. Gattuso has a contract and he will respect it."