The Argentina international has been the subject of widespread media speculation during the transfer window, with the likes of Manchester United and Paris Saint-Germain heavily linked with the 26-year-old.
PSG president Nasser Al-Khelaifi claimed a fortnight ago that their interest in the player had ended due to Real demanding a hefty fee.
In a press conference on Thursday, Ancelotti revealed that Di Maria had stated his wish to move on, which will alert his potential suitors.
"Di Maria has asked to leave and rejected an offer from club," he said. "[But] if he does not find a future solution he stays, no problem."
Sami Khedira has also been linked with a move away from the Santiago Bernabeu and Ancelotti confirmed that the Germany international has decided against agreeing a new contract, possibly opening the door for a transfer in the near future.
"Khedira has one more year and has rejected new deal," said Ancelotti.
"It is different than Di Maria as he has not asked to leave."
With Real preparing for their Supercopa de Espana second leg against Atletico Madrid on Friday, Ancelotti believes star man Cristiano Ronaldo should be available, after being withdrawn at half-time in Tuesday's first leg, which ended 1-1.
"Ronaldo has trained well," he said.
"He had a normal session and is available. He could start.
"To win at the [Vicente] Calderon, we must play with intensity and faster than the first leg. Atletico has the advantage of the positive results obtained and will play as in the Bernabeu."