Paolo Di Canio's side have had a bid accepted for the 18-year-old defender but face competition from last season's Ligue 1 runners-upLe Havre president Jean-Pierre Louvel has challenged Olympique de Marseille to match Sunderland's offer for Benjamin Mendy.
Paolo Di Canio's side agreed a fee for the left-back in June, but the player is thought to be keen on a switch to the Ligue 1 runners-up instead.
However, Louvel insists that a move to the Stade Velodrome will not be happening unless Marseille can strike a deal that rivals Sunderland's offer.
"We have an agreement with Sunderland, but not with Marseille," he told L'Equipe. "There are no offers at the moment. Nothing has materialised.
"Marseille's offer should not be lower than that of Sunderland's. Everything will depend on Marseille's proposal.
"About the price, I have a confidentiality agreement with the English club, so I cannot tell you anything. But what is certain is that Marseille's offer should not be below that of Sunderland."
Louvel was also unconcerned by reports that the 18-year-old had already undergone a medical at Marseille.
"It does not shock me that he goes to visit Marseille," he added.
"That sounds very normal for him to make his choice. But he knows that to seal a deal with a club, you have to have the green light from Le Havre.
"And I repeat that we do not negotiate below what Sunderland have offered."