The Daily Star says Arsenal have been keeping close tabs on Payet's situation at the Hammers and could make a move to land him in next month's transfer window.
And United have also joined the race to sign him and Old Trafford bosses have asked sources close to Payet to keep them informed of his situation.
United also have the financial power to blow the Gunners out of the water and would be willing to hand Payet a deal worth around £220,000-a-week.
Payet said: “The situation at the club affects me, but I'm an ambitious person. I'm in a fight with my club and I'm giving everything for them, to get out of this difficult situation - but I'm not closing the door to anything.
“I miss the Champions League. I've got some great years ahead of me and I want to enjoy them by playing in important competitions.
“If I'm forced to leave West Ham, it will be done according to the rules – the club will have its share of the cake. My coach understands the situation does not suit me."