The experienced midfielder's current deal runs until the summer of 2012, but he's eager to sign a contract extension with the Serie A champions
The 33-year-old's current terms with the San Siro club are due to expire in 2012, but the player is keen to end his career with Milan and wants to wrap up negotiations sooner rather than later.
Nevertheless, Gattuso wants clarity on his future and could well decide to leave at the end of the season if no agreement regarding a new deal is reached.
The former Rangers enforcer has previously been linked with Russian giants Rubin Kazan, while Anzhi Makhachkala are also keen to lure him away from Serie A.
The experienced World Cup winner has played an important role in his side's Scudetto win this term, and currently sits in 573rd spot in the Castrol EDGE Rankings.