The 26-year-old midfielder plays for French club Chateauroux in Ligue 2, but they have agreed to let the player take his opportunities in Britain.
Kevin Blackwell wants additions to his squad, and is keen to give the African a chance.
Coulibaly will join up with the Leeds squad for training and could be given a run out with the reserves.
He was with Mali in the African Cup of Nations in the same squad as Spurs striker Fredi Kanoute.