The former Juventus and Italy boss is available after he split with Chelsea. But, the way things ended for him in England could be little cause for concern.
However, Conte's return of three titles in as many seasons with Juve makes him an attractive prospect for any Serie A side, and he would perhaps offer a level of tactical maturity the more inexperienced Gattuso cannot yet match.
"I can't think of Antonio Conte or who will arrive," Gattuso replied in September when asked if the spectre of the man persistently linked with his position was affecting his work.
Should he be the one preferred, Milan might have to make a move sooner rather than later as Real Madrid are also reportedly keeping tabs on the 49-year-old.
When it comes to experience there is no option left other than, former Arsenal boss Arsene Wenger.
The Frenchman was touted as an option soon after Milan's recruitment of Ivan Gazidis as chief executive from Arsenal, where the pair worked together for almost a decade.
The decorated Frenchman this week revealed he would be ready to return to work in January after receiving offers "from all over the world", with Bayern Munich and Madrid both mentioned as possible destinations. He has also been linked with a job at PSG.
Roberto Donadoni could provide a safe pair of hands for the Rossoneri hierarchy to stave off further instability.
The 55-year-old former Milan midfielder left Bologna in May with his reputation generally enhanced from a three-season stay, having previously spent a similar stretch with Parma.
Donadoni's failures in charge of Italy and Napoli do cast some doubt over his ability to handle grander responsibilities, but his ties to Milan are as strong as those making the decisions.
Having quit Real Madrid in July, Zinedine Zidane may have hinted he is not ready to get back to football for at least a year. But, Milan's new project could tempt the Frenchman.
Milan's prolonged absence from the Champions League has robbed them of the glamorous sheen that Zidane could certainly replenish as no available head coach knows as much about winning in Europe than Champions League specialist Zidane.
The prospect of proving he is capable of claiming silverware without a readymade squad could intrigue the ex-Serie A star, but his bond with the Bianconeri makes the idea of a union with Milan complicated
Zidane, who is also being linked with Jose Mourinho's job at Manchester United, clearly has the insights that could turn a team rippling with unrealised potential in genuine contenders.
After leaving Monaco, earlier this month, Leonardo Jardim is reportedly on the hunt for a new project. The Portuguese has a proven skillset attuned to fast-tracking a young bunch into unexpected title winners.
Jardim's entertaining side led by Kylian Mbappe toppled Paris Saint-Germain in Ligue 1 and captured Europe's attention in 2016-17, achievements that will have not gone unnoticed by the movers and shakers within the continent's top clubs.
Having known to develop youth and Milan boasting the likes of Gianluigi Donnarumma, Patrick Cutrone and Franck Kessie, Jardim will definitely give them further push in their careers.