The former midfielder was placed in charge of the San Siro club back in November, after Vincenzo Montella was sacked.
Gattuso was given a contract until the end of the season when he agreed to take the reins and it was reported Milan would look at other more long-term targets in the summer.
Chelsea boss Antonio Conte was said to be high on their shortlist, while Carlo Ancelotti was also considered an option.
But now, according to Calciomercato, Milan are ready to end their search for an alternative by rewarding Gattuso with a new contract.
Gattuso has steadied the ship since taking charge and Milan are unbeaten since Christmas Day.
The Italian club are prepared to extend the 40-year-old’s contract to at least 2019, although they haven’t ruled out making it longer than that.