The Nancy striker has been linked with a move to Parkhead, with the Glasgow giants set to confirm Tony Mowbray as their new manager.
Fortune impressed while on loan at West Brom last season and the French outfit have warned competition is fierce for his signature, with the Tigers, Cottagers, Blues and Wolves all interested in the 27-year-old.
Nancy sporting director Nicolas Holveck told the Daily Record: "We have several English sides showing an interest and there is definite interest from Celtic.
"But they have to move fast because we already have official offers in from English sides and value him highly.
"We want four million euros, nothing less or he won't be sold.
"He has two years left on his contract here so we don't need to sell him.
"He's at the peak of his career and will be a valuable asset to any side that gets him but they have to pay our fee or there is no sale."