Reports claim Zaragoza have contacted Toffees boss David Moyes in a bid to establish an asking price for the Spaniard, who made his name at Rangers before later joining Real Sociedad.
Arteta is contracted to the Goodison Park club until June 2009 and the player's agent Inaki Ibanez has recently held talks with The Toffees over an extension.
Ibanez is expected on Merseyside this week in order to resolve the player's future.
Arteta has been an integral part of the club's successful quest for Uefa Cup football, scoring nine goals in 34 Premiership appearances.
Zaragoza, keen to bolster their midfield for next season,
have also been linked with a move for Juventus' Olivier Kapo, who insists his future
remains in the Italians' hands.
Kapo has impressed while on a season-long loan at Levante, reportedly catching the eye of both Zaragoza and Real Betis.
Levante could also still tie up a permanent deal for a player valued at €3million (
£2million), but Kapo is determined to resist the speculation.
"My contract in Italy does not finish until 2008 and
it all depends on Juve," Kapo told the Spanish press.
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I say we should keep Kapo, he's a good squad player, he's been with Deschamps, when he was at Monaco.