The 26-year-old has been a key performer for Livi this term, scoring one of their goals in the Scottish League Cup final win over Hibernian.
He is coming to the end of his contract and a host of clubs are monitoring his situation with interest.
Livi have not given up hope of keeping McAllister at Almondvale, but he is likely to assess his options over the course of the summer before making a decision.
Owls boss Chris Turner is keen to reshape his squad over the summer and has admitted McAllister is just one of many faces he is considering.
McAllister arrived at Livi in the summer, having been released by Aberdeen, and he has proved a key player for the West Lothian outfit and they may well be regretting only handing him a season-long contract.
