Leeds United are trialling the Northern Ireland international and former Guinea international Mo Camara.
Both have been going through their paces at Thorp Arch for the past few days and are hoping to earn a contract.
Leeds boss Simon Grayson said: "It is promising that I have a Northern Ireland international wanting to play for this club, as does Mo Camara who has played at the highest level."
Gillespie is 34 this month.
His Bramall Lane contract was terminated by mutual consent