Arsenal have reportedly pinpointed the Real Madrid star as the ideal man to solve their defensive midfielder problem.
The defensive midfielder traded fellow La Liga side Real Sociedad for Madrid 18 months ago but currently finds himself out of the first-team due to competition for places.
With Luka Modric coming back from injury and the signing of Lucas Silva now being confirmed, Illarramendi is further likely to struggle for game time and questions have been raised over his future.
The Spanish publication confirm that the Gunners have made an official approach for the player as boss Arsene Wenger looks to strengthen during the winter market.
Illarramendi, however, is ignoring the speculation for now and says he is awaiting his current club to tell him his options while stating his desire to remain at the Santiago Bernabeu.
"At the moment I don't know if he has been signed or not. If he [Lucas Silva] comes or if the club says something,they'll tell me what my options are. Right now I don't know anything,” he told AS.
“The club hasn't said anything and I'm just thinking about the Córdoba game. I am very happy here at Madrid. The club hasn't said anything and as things stand I'm a Madrid player and I want to stay here.”
Illarramendi has played just 932 minutes worth of football this season, an incredibly low figure for such a talented player.
A move to North London would certainly be a sound choice for both parties, with Illarramendi all-but guaranteed a first-team spot and the Emirates outfit going to some way to solving their midfield dilemma.