Tigers boss Phil Brown has confirmed a bid has been lodged with the French club Nancy, believed to be in the region of £2.5m.
Fortune's representatives will now meet City chairman Paul Duffen next week to thrash out personal terms.
He told the Hull Daily Mail: "Marc-Antoine Fortune is a player that we're interested in.
"We have discussed terms with his club and I would say we're probably one of three serious contenders. We've done our business with his club and we remain hopeful.
"He's someone who caught the eye and captured everyone's imagination in the second half of last season."