Madrid were ready to cash in on the 24-year-old following the arrival of Lucas Silva earlier this month, with Athletic willing to break their transfer record of €12 million for the holding midfielder.
However, Illarramendi has made it clear he does not want to leave the capital just yet and Ancelotti will give him another chance to prove his worth in the Liga match against his former club Real Sociedad at the weekend.
"Illarra had an offer from Athletic Bilbao," Ancelotti said at a press conference.
"But the player has made it clear that he is feeling happy and satisfied at Madrid. He has evaluated his situation and has decided to stay put.
"Both the club and I are very happy with Illarra. He might not have played much, but he has always behaved very professional and proven to be a reliable option.
"He will feature from the start against Sociedad at the weekend."
Illarramendi joined Madrid from Sociedad in July 2013 for a transfer fee of €32.2 million, but he has so far been unable to become an undisputed starter under Ancelotti.
The midfielder has a contract with the Bernabeu outfit until June 2019.
