The goalkeeper joined the Scottish Championship leaders during the January transfer window.
The 27-year-old signed a six month deal with the Scottish Championship leaders after leaving Polish side Lech Poznan, but had failed to make a single appearance for the Light Blues and was only selected for the bench on one occasion.
STV claims that the coaching staff were not overly impressed with what they saw from Gostomski, and now it appears that the player has been left to find a new club - though he will not be able to until the summer window opens.
The news of Gostomski's departure is unlikely to unsettle Warburton's squad too much, given the minimal contribution he made to the first-team during his time at the club.
Summer signing Wes Foderingham has played in every single game that the Gers have had this term - and has done an exceptional job, helping the side keep the best defensive record in the division - while understudy Cammy Bell has proved during his time at Ibrox, as well as at Kilmarnock previously, that he is more than capable of stepping in between the sticks if required.