The Basque club are in talks with Real Madrid, keen to tempt Illarramendi back by matching terms offered by Premier League clubs.
According to Spanish national outlet Marca, the Basque club managed by David Moyes are prepared to match a reported €15 million bid from Liverpool, and the salary requirements of the 25-year-old midfielder.
Whilst there is the speculation Illarramendi might prefer a move to the Premier League, rather than a return to his former club, Real Sociedad are said to be prepared to sell one of two existing stars, to fund their move.
The two players linked with possible exits, to pave the way for Illarramendi to arrive, are Esteban Granero and Chori Castro, although it would seem unlikely that La Real would strengthen in one area, only to weaken themselves in others.
Regional newspaper Diario Vasco have also underlined the importance of Real Sociedad moving for Illarramendi, but have acknowledged that along with the rival bid from Liverpool, there's also interest from Tottenham Hotspur.
In addition, given that Illarramendi is now considered surplus to requirements at Real Madrid, bids are also expected to be received from Italian giants Inter Milan and Juventus. Likewise, speculation continues that Athletic Club Bilbao could also throw in an offer, having already done so last January.
Real Sociedad defender Iñigo Martinez has also offered his thoughts, hopeful his good friend will return from Real Madrid. He explained: "You can't doubt the quality of Illarra. He's a player any club would love to have, most of all us."
Conscious the midfielder rejoining would provide La Real with a great boost, Martinez added: "With Asier here at Real Sociedad the team would change a lot and he'd be a very welcome addition."
Real Sociedad were held to a 0-0 draw away at Deportivo La Coruña, in their opening encounter of the 2015-16 campaign in La Liga. If they can manage to resist the interest from England and Italy for Illarramendi, getting the player back would be a marvellous addition, as Moyes aims to steer his team to a European finish in the league this season.