Under-pressure Gattuso retains 'great respect' for Leonardo
Reports in the Italian media claim Leonardo, who returned to the club in July, plans to replace Gattuso with ex-Italy boss and former Rossoneri midfielder Roberto Donadoni.
The fresh speculation comes in the wake of the weekend's late derby loss to Inter that left Milan with 12 points from their opening eight Serie A fixtures.
Gattuso denied there are problems between him and Leonardo while dismissing the effects of the increasing scrutiny surrounding his position.
"I'm a professional coach, I know I'm questioned when results don't come in," Gattuso told a news conference.
"I have lived a lot worse pressure with Crete [in Greece] and Pisa. Here is nothing compared to the past.
"I have a relationship with Leonardo and [director Paolo] Maldini. We always confront each other honestly. We tell each other how we see it without any problems.
"Sometimes we don't agree but there is great respect and we speak face to face."
The Coach on the derby: "If you play to take home a 0-0 draw you field the team in a 4-5-1 and park the bus. I don't think that this was the case. You can say that #ACMilan didn't play a good game but you can't say that we took the field to draw the derby"#MilanBetis
— AC Milan (@acmilan) October 24, 2018
Gattuso was speaking ahead of a home meeting with Real Betis in the Europa League that could potentially seal Milan's progress to the knockout rounds.
Pepe Reina has started each of the club's two European victories this term and could again relieve Gianluigi Donnarumma following the under-fire goalkeeper's costly error against Inter.
The teenager's failure to deal with Matias Vecino's cross – he initially moved off his line to suggest he was coming to claim the ball, only to then change his mind - gifted Mauro Icardi the stoppage-time winner on Sunday, but he continues to have Gattuso's support.
"I don't agree that he should be on the bench," Milan's head coach said.
"Before the derby you all said how he was much more reliable than last year. I make the choices and I don't follow the fans, despite the respect I have for them."