Seri, 26, has been a star for Nice ever since his 2015 move from Pacos de Ferreira, notching 12 goals and 20 assists in 103 Ligue 1 appearances to date.
The Ivorian international, who has 16 caps to his name, was strongly linked with a move away last summer but ended up staying, though speculation is once again rife this summer.
Sky Sports recently reported that Arsenal, Chelsea and Manchester City were all keen on Seri, but West Ham United were plotting an ambitious move for the midfielder, who has a £35million release clause in his contract.
West Ham certainly need midfield reinforcements, and the diminutive Seri would fit the bill, but it seems that the Hammers won't be able to bring him to the London Stadium this summer.
Nice-Matin report that Seri does want a move to the Premier League, but doesn't want to join West Ham as they don't have the standing he is looking for, compared to an Arsenal or a Chelsea.
Those clubs being able to offer European football was always going to be important in the battle for Seri's signature this summer, with the midfielder seemingly ready for the next step.
However, West Ham would be wise to keep tabs on the situation. If neither Arsenal or Chelsea move to sign him this summer, the Hammers may be well positioned to offer Seri the Premier League move he wants – even if it isn't the top six team he's looking for just yet.