Fortune, who spent last season on-loan at West Brom, has Wolves, Albion and Hull City all chasing his signature.
The Express & Star says the Baggies are keen to tie him to a permanent deal and could land him for £1.5m, having negotiated a binding transfer fee with the French club when they signed the player on loan.
But Wolves have also enquired about the hard-working forward while Celtic - who want Baggies boss Tony Mowbray as their next manager - are also interested.
Nancy are said to want £3m for Fortune after interest hotted up, with the £1.5m figure exclusive to Albion. But they are under pressure to raise money to fund their own transfer ambitions, so are likely to negotiate.