The Italian tactician previously enjoyed an incredibly successful spell in charge at the Stadio Giuseppe Meazza, where he also spent time as a player, whereas he has never coached the Giallorossi, though he remains a popular figure at the club since his time there as a player.
Speaking to Corriere dello Sport, Ancelotti admitted he would be keen to take the reins at either of the Serie A clubs.
“I love Roma and the city,” the former Chelsea boss began.
“I would love to return to the club one day.”
The 56-year-old went on to reveal just how close he came to rejoining the Rossoneri in the summer, but a medical issue dictated he could not take the job, which led to Sinisa Mihajlovic taking charge at the San Siro.
“I would also like to return to Milan at some point. I came close to going back in the summer, but I needed to take some time off as I required surgery.”