The Spanish club's sporting director Braulio Vazquez has been in touch with Arteta's agent, Inaki Ibanez, and Everton could listen to offers for the midfielder as they attempt to reduce their ?45million debt before the start of next season.
Arteta, who arrived at Goodison Park from Real Sociedad in 2005, signed a five-year deal last year worth ?60,000 a week.
Homeward bound? Arteta has been linked with a move to Spain for a few years
Atletico Madrid are also monitoring 29-year-old Arteta's situation.
Manager David Moyes is desperate to keep his squad together but his knows his hands are tied.
Manchester United target Jack Rodwell will be allowed to leave for around ?20m while north London rivals Tottenham and Arsenal are keen on England full-back Leighton Baines.
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