Illarramendi, 24, is being forced out the exit door at the Bernabeu following the €14 million capture of Brazilian counterpart Lucas Silva, with Madrid said to be keen to offload him this month.
La Liga rivals Bilbao have lodged an offer of €25 million which the club are eager to take, but the former Spain under-21 international would prefer to remain at Real for the rest of the season and weigh up his options in the summer.
The report comes after Marca claimed last week that Arsenal had approached Illarramendi about a potential summer switch, which the out-of-favour midfielder would accept “without thinking about it” given his Premier League ambitions.
The fact that the report also claimed Illarramendi was reluctant to agree terms with Bilbao suggests that there could well be some truth behind the rumours, although it has been stressed that no discussions have taken place between the Gunners and Real at this point.
AS adds that there has been interest from England, without mentioning specific clubs, but notes that potential suitors are reluctant to match the €25 million asking price.
In addition, a return to former club Real Sociedad has been mooted, but the Basque outfit’s financial situation would restrict the deal to a six-month loan switch.
Signed from Sociedad in the summer of 2013 for €32.2 million, Illarramendi was a regular starter during his first season at Real, but has been in and out of the side so far this term, despite some tipping him for a first senior national team call-up prior to the World Cup.
At his best in his favoured holding role, the Spaniard’s age, pedigree and promise would make him a fine addition to the Arsenal squad, but whether Arsene Wenger will be able to lure him to the Emirates Stadium in the near future remains to be seen.