A number of Premier League clubs have been keeping tabs on Remy's situation this summer, with the frontman making it clear that he would be keen on a move to England.
Stoke stepped up their pursuit earlier in the week, inviting Remy to the club for talks and showing him around their training ground.
The 23-year-old was impressed by what he saw and heard at Stoke but admitted he would take his time before making a decision on his future.
And it now seems Stoke are out of the running, with Remy's immediate focus on Nice's opening Ligue 1 game of the season against Valenciennes on Saturday night.
Speaking about the player, Nice general manager Patrick Governatori told L'Equipe: "It will not be sorted out with Stoke.
"I hope he will score on Saturday night. If he can play a good match, he could get the opportunity to be in the French starting XI (against Norway on Wednesday)."
Reports in France suggest scouts from Tottenham, West Ham and Sunderland will be present to watch Remy in action for Nice.
It is understood that Remy would only be willing to part with Remy for a fee of 14million euros (£11.7m).