The 31-year-old, nicknamed Ringhio (Snarler), has made more than 250 league appearances for the San Siro side since joining from Salernitana in 1999.
However, the former Rangers enforcer - who missed large parts of the 2008/09 campaign through injury - is believed to be upset with Ancelotti's departure from Italy.
And he has now revealed that he is not guaranteed to still be a Milan player by the start of the new season, adding that a move to England would interest him.
"I like the Premier League. The Premier League is the best league for me, for my characteristics," he said in the Daily Mirror.
"I don't know what will happen. I have been at AC Milan a long time and it's not easy to go away, but we'll have to see.
"Chelsea are a big, big team but working with Ancelotti is a good feeling. We have worked together for eight years and he is for me a second father.
"He is a great person, and a great manager."
CHELSEA FANS! Check FourFourTwo.com’s ever-expandinginterviewsarchive for more stuff to read:
Web Exclusives Kerry Dixon, Guus Hiddink
One on One Gianfranco Zola, Nicolas Anelka
Boy's A Bit Special Michael Mancienne, Scott Sinclair
Perfect XI Ruud Gullit, Marcel Desailly
Celebrity fans Vidal Sassoon
And Another Thing Being a Big Four fan
Plus! Ruud Gullit on Weekend Wonders and Chelsea on Talentspotter
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
