The 58-year-old spent most of his playing career with the Giallorossi, making 171 appearances for the Italian capital club between 1979 and 1987.
Now out of work after being sacked by Bayern Munich last month, Ancelotti is being linked with numerous roles, including those at AC Milan and the Italy national team.
Though Ancelotti remains unattached at present, the Italian admitted that he could have been managing his former club following Rudi Garcia's dismissal were it not for his commitment to Bayern.
"[President James] Pallotta called me two years ago to bring me to Roma, but I had already signed for Bayern," Ancelotti told Il Messaggero.
Eusebio Di Francesco is currently at the Roma helm.