The Bundesliga side are hoping to cash in on the controversial striker this summer seeing that his contract is due to expire at the end of the season.
Werder have recently rejected a loan bid from West Ham, but it looks as though they might just get rid of the Austrian after all.
According to Bild, both Valencia and Real Sociedad are keen on the 24-year-old attacker and they are expected to make their interest concrete in the coming weeks.
While los Che are searching for attacking reinforcements after selling Roberto Soldado to Tottenham, la Real aim to add more bodies to the squad as they prepare for the Champions League campaign.
Marko Arnautovic has been heavily criticized for his unprofessional behaviour while at Werder, but he has still managed 5 goals and 6 assists in 26 Bundesliga matches last term.