“My wish is to leave the club,” said the Italian after meeting president Naser al-Khelaifi.
“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.”
Ancelotti is widely expected to replace Jose Mourinho at Real Madrid in the summer with the Portuguese tipped for a return to Chelsea.
“We met with the president and with Leo (sporting director Leonardo). We’ll have to wait a few days,” added Ancelotti, who this season led PSG to a first title since 1994.
“There are possibilities. Real Madrid is one. But I have a contract here and I am waiting for the club to decide.”
Leonardo confirmed that Ancelotti, 53, had asked to leave.
“What happened was that Carlo has asked to leave for Real Madrid. We want to keep him,” said Leonardo.
“He has another year on his contract with us. No decision has been made.”
Former Chelsea and AC Milan coach Ancelotti has spent just 18 months at the club from the French capital.
But rumours that he is set to replace Mourinho at Real when this season finishes had been gathering pace in recent weeks.
Those were only enhanced on Sunday morning when several Spanish newspapers claimed the Portuguese boss would leave before the end of the current campaign.
Madrid sports daily Marca ran the headline “he is going to Chelsea” on Sunday morning, adding that “Real Madrid could make his goodbye official this week”.
Another Spanish newspaper, broadsheet El Mundo, also reported that Mourinho may not even be in charge for Real’s final two games of the season against Real Sociedad and Osasuna.
“Madrid want to sack Mourinho now,” it claimed.
“The board and the president, Florentino Perez, have had enough after the defeat in the final of the Copa del Rey and the tense situation in the dressing room, and are planning to bring to an end the Portuguese’s reign immediately.”
Ancelotti’s first six months at PSG were largely disappointing as he took over a team at the top of Ligue 1, only to see them overhauled by Montpellier to miss out on the title.
However, this season he delivered on the club’s twin objectives of winning the league and reaching the Champions League quarter-finals.
He was greatly aided, though, by a huge financial investment from the Qataris that allowed PSG to sign the likes of Zlatan Ibrahimovic, Thiago Silva and Ezequiel Lavezzi, as well as bringing in David Beckham on a short-term deal in January.
Ibrahimovic said he wanted Ancelotti to stay in charge.
“I wouldn’t want him to leave. He is a fantastic coach,” said the Swede.
“I hope he stays, there is a great project here and a fine team. I have scored lots of goals because of him.”
Ancelotti won two Champions League titles and one Serie A crown with AC Milan while he also completed a league and cup double at Chelsea.
He has won titles in three different countries and is one of the most respected coaches in European football.