The 22-year-old was enjoying a loan spell with Livingston when, in January, he was recalled following Tom Heaton's serious knee injury.
Sarkic has been at Villa since 2015 but has never player for the first team, instead being sent out to other clubs for experience.
“I think that there will be little space for a real chance in Aston Villa in the future, so I plan to go, despite the club's desire to extend my contract, which expires at the end of June.
“Now I am diligently preparing for the status I want, and that is the first goalkeeper.
“There is interest, both in England and abroad. Aston Villa is now one of the four richest clubs. The ambitions are great, and the competition is already huge."