The 29-year-old playmaker's stock is rising virtually every time he kicks a football and he netted again for France in Euro 2016 on Wednesday, following his last-minute wonder goal in the 2-1 win over Romania on Friday night.
His compatriot, Lacazette, has been heavily linked with a switch to West Ham this summer and, according to Gianluca Di Marzio, a £32 million bid was lodged by the Irons for the in-demand Lyon striker this month.
However, the Ligue 1 outfit are reportedly holding out for at least £40 million for their prized asset and The Mail have suggested that West Ham are considering whether to pull their interest in order to keep Payet happy as the club's most important player.
If true, it would speak volumes for how highly the East Londoners rate the Frenchman, with whom Real Madrid are reportedly weighing up a £40 million bid for (Le 10 Sport).
Payet, a £10 million summer signing from Marseille last summer, scored 12 times and set up 14 in all competitions last season, with his form in France being a continuation of what was a superb maiden campaign with the Premier League side.