The Frenchman progressed through the youth system at Nantes and made his senior debut during the 2006/07 Ligue 1 season.
He left France for Belgium in August 2011, signing a five-year contract with Liege, but Craven Cottage manager Jol is desperate to bolster his squad in the January transfer window.
Vainqueur's agent Nico Vaesen said: "Fulham's style suits. They've a Dutch coach who likes a passing game."
Jol brought in French-born Senegal midfielder Mickael Tavares on a short-term contract in October after losing Mahamadou Diarra.
However, the Mali international has returned from his knee problem quicker than expected and is back in the Fulham team.