The Argentina international has been heavily linked with a switch to Old Trafford in recent weeks and was left out of the Real squad for Friday's Supercopa de Espana second leg against Atletico Madrid.
Paris Saint-Germain are also among Di Maria's potential suitors, but Financial Fair Play restrictions appear to have halted their plans to bring him to the French capital.
However, the 26-year-old's departure now appears to be imminent.
"Angel di Maria has said his goodbyes," Ancelotti is quoted as saying by Sport. "It's not official but the matter is resolved - it was his decision to leave."
World Cup winner Sami Khedira had also been linked with a move away from the Santiago Bernabeu, but Ancelotti has insisted the German is going nowhere - at least for the time being.
"He is happy here and he is staying," he added.
Arsenal had appeared to be among the frontrunners for Khedira's signature.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.