The 26-year-old currently plays for Ukrainian side Metalist Kharkiv but is keen for a new challenge and may join up with compatriot Artur Boruc at Parkhead.
Gancarczyk will have a chance to impress the Celtic coaching staff during a training spell with the club this week.
Lee Naylor is Celtic's first-choice left-back and has had little competition for his place, however Gancarczyk would be expected to push the Englishman for selection should he secure a move.