Gattuso played under Ancelotti during his celebrated eight-year spell in charge of the Rossoneri between 2001 and 2009, twice winning the Champions League.
"It will be a very tough game," Gattuso told a pre-match news conference. "I spoke yesterday with Carlo Ancelotti.
"Carlo and I have a great relationship. He was more than a coach to me, I would call him during my hardest times. I can only learn from him.
"The press says we have different characters but Carlo as a player was a fighter, the last man to surrender.
"As a coach he was similar to [the great former Milan boss] Nereo Rocco. He would chat with the players after the training session, stay with them and I have never heard anyone say anything bad about Carlo."
Gattuso saw Antonio Conte linked with his post during the close season and when asked whether Milan could mount a genuine Scudetto bid, he suggested the type of stability Ancelotti brought to the San Siro would need to be rediscovered following a turbulent period.
"Are we title contenders? I think we still have a long way to go," the 40-year-old said, having recently received assurances from Milan's owners over his future.
"Our goal is to improve the standings of last season and work hard to reach the fourth place.
"We need an identity. I don't know how many coaches have been here in the past years, six or seven. It's easier to work when you have continuity.
"When you change too often, everything becomes more complicated."