19 year-old Gillespie was with Liverpool until the end of last season, having been a regular scorer for the Anfield club's youth and reserve teams. He was released at the end of last season, and joined Bristol City after a short trial, in which he scored seven goals in three reserve games.
Gillespie has already played at Whaddon Road this season, scoring twice for Bristol City reserves in a 4-4 draw.
He has been unable to break into the City starting eleven, having not been able to dislodge Leroy Lita, Paul Heffernan, or Steve Brooker from the Ashton Gate side's team. He has started two games, and made eight appearances as a substitute.