The 26-year-old arrived Parkhead in January from Dundee on loan until the end of the season as cover for the initially injured Craig Gordon, but with the Scotland international back on his feet and in the starting XI, Bain could be attracted by the bright lights of the Premier League.
With Premier League football all but guaranteed for Nuno Santos' side next season, Bain could fancy his chances of forcing himself into the starting lineup, or even make do with a place on the bench in the highly-rated English top-flight.
Hoops boss Brendan Rodgers wants to land the former Aberdeen man on a permanent basis by summer, while Stoke City, Hearts, and Hibs are also keen on the shot-stopper who will become a free agent soon, as reported by the Sun.
Having spent all his career in Scotland, changing environment and moving to England could appeal to Bain, and the Potters could also interest him, even if they will likely be playing in the English Championship next season.
With Jack Butland certain to move on if Stoke fail to escape the drop, Bain has all it takes to fill his boots, and Stoke will likely firm up interest if the need arises.
Both Wolves and Stoke are attractive options to the Hoops man, especially if they are both playing in the Premier League next term, and Celtic might have to guarantee him a starting spot if they are to hold on to him beyond his loan deal.
From the look of things, Gordon remains first-choice going forward, and Bain's future at the Parkhead is up in the air, especially if the England links keep getting turned up a notch in the coming months.