Illarramendi, 24, joined from Real Sociedad for a fee of 30 million euros (22.49 million pounds) in July 2013 as a long-term replacement for Xabi Alonso but even though Alonso has moved on Illarramendi has been unable to hold down a starting place.
The imminent arrival of another defensive midfielder, Brazilian Lucas Silva, has prompted speculation Illarramendi will leave, with Real's struggling La Liga rivals Athletic Bilbao and English Premier League side Arsenal reportedly interested in signing him.
"We don't have that idea at the moment," Ancelotti told a news conference previewing Real's La Liga game at Cordoba on Saturday.
"He (Illarramendi) hasn't played much recently but that does not alter the confidence we have in him and his importance to the dressing room and the team," added the Italian.
"I think to have a motivated team you need players who are available and professional in all the training sessions and Illarra is one of them.
"If I need him I will play him as I have total confidence in him operating in central midfield."
One of the players who is ahead of Illarramendi in the midfielder pecking order is Isco, who has shone since getting more playing time due to an injury to Luka Modric.
Ancelotti said Isco was suffering from muscle fatigue and was unavailable for the Cordoba game and either Illarramendi or Sami Khedira would replace him in the starting lineup.
La Liga leaders Real, who have a game in hand, are a point clear of second-placed Barcelona, who play at Elche on Saturday, at the halfway point of the campaign.
Champions Atletico Madrid, who host Rayo Vallecano on Saturday, are three points behind Barca in third.
(Writing by Iain Rogers, editing by Martyn Herman)
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