Nancy sporting director Nicolas Holveck said: "We have accepted three offers, all from English clubs.
"All are in excess of 4m euros and, with add-ons, one is approaching the 5m euros mark."
Hull have already held discussions with Nancy and the Tigers manager, Phil Brown, claimed that his club were one of three serious contenders for Fortune's signature.
"We are happy to allow the player to begin negotiations with these clubs and we expect the transfer to be formalised by Monday," added Holveck.
"It's still possible he could move to Celtic but they have yet to make an acceptable offer."