The football news magazine claim on their website website that the top flight duo are joined by rivals Southampton in demonstrating concrete interest in the versatile attacking sensation.
The trio may be looking to secure a cut-price deal for the French youngster, who can also play as an out-and-out striker, with his contract set to expire in a years time.
France Football report that Karamoh has told the club he does not want to extend his current deal.
However, the Premier League sides may need to work quickly with the magazine claiming that his agent has already set out a deal with St Etienne, which can be signed six months prior to the end of his current contract.
Karamoh made 35 appearances for Caen in Ligue 1 last season, scoring five goals and contributing four assists as they narrowly avoided relegation with a 17th placed finish.
West Ham are known to be in the market for a striker this summer, although co-chairman David Gold has insisted that their priority will be securing at least two proven Premier League forwards.
Meanwhile Everton boss Ronald Koeman looks set to overhaul the entirety of his attack this summer, with the futures of Romelu Lukaku and Ross Barkley in doubt, while Fanatik claim that 58-cap Belgian winger Kevin Mirallas could see himself offloaded this summer.