Ancelotti had a meeting to discuss his future with club president Nasser Al-Khelaifi and sporting director Leonardo on Sunday.
"Yes, we had discussions, he asked to depart for Real Madrid," Al Khelaifi told beinsport.fr.
"I said it is not possible because he has a contract for one year more, so that is our decision.
"It is his problem, it is not our problem. We have offered him another year more on his contract as well as the one he has. When you have a contract, everyone is normally obliged to honour that."
Ancelotti confirmed: "My wish is to leave the club. I have asked the club to leave. We are going to wait for a response from the club who are going to take a few days to decide."
Earlier this week, Al-Khelaifi said he rebuffed an approach from Madrid's sporting director for Ancelotti.
Ancelotti steered PSG to their first French league title since 1994 last week and Madrid coach Jose Mourinho is expected to leave at the end of the season.