The Italian joined the Spanish giants this summer from Paris St Germain, signing a three-year deal with the nine-time European champions.
"A lot of people have asked me about the possibility of coaching Roma or the (Italy) national team in the future," Ancelotti said to Sky Sport Italia. "I don't know - I could even decide to retire after my experience at Real Madrid."
The 54-year-old played at Parma, Roma and AC Milan before turning to coaching in 1995.
Ancelotti won a league and cup double with Chelsea in his first season in charge at Stamford Bridge before he was sacked in May 2011 despite finishing second in the Barclays Premier League.
He was also a two-time Champions League winner during his decade at Milan, and led PSG to the Ligue 1 title last term.