The Owls have offered Lavery a new deal to remain at Hillsborough, but the attacker is believed to be considering his options.
Wednesday have high hopes for Lavery’s future at the club, but he has now reached the age of 23 and still has not broken into their first team.
Lavery was loaned out to Portsmouth last season, with Carlos Carvalhal deciding that he was not ready to play a role for Wednesday.
The Owls front man seems unlikely to break into Wednesday’s team for next season, and his lack of first-team action has reportedly made him think that his future may be better off spent elsewhere.
Lavery is apparently eager to move on, and he is considered unlikely to sign a new deal with the Yorkshire side.
Coventry City are one of the sides believed to be interested in signing Lavery.
Wednesday will be due some compensation if the front man does move on, as he is still under the age of 24.
Wednesday have also offered new deals to both Jose Semedo and Lewis Price.