The 29-year-old was signed by Slaven Bilic from Marseille in 2015 and signed a five-year deal. After impressing in his debut season, the midfielder has continued his form for the Hammers this term, despite the club's struggle.
Wenger had earlier confirmed that the north London club watched Payet in action when he was at Saint-Etienne, however, they decided not to make an approach for him. Now, the former Marseille man has expressed his desire to play in the Champions League, something he can fulfil if he decides to join Arsenal over United in January.
"I read that Wenger considers me the missing piece of the Arsenal's game, but he's never told me that," Payet told RMC, as quoted by Goal.com.
"We conceded five or six at home against them. When you see them playing, as a technical player, you could only have fun in that team. They're candidates for the title every year."
"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," he added
According to The Sun, the Arsenal manager may consider an approach for Payet in the January transfer window. The Gunners are not the only side keen on securing his services as the Mirror has claimed that Jose Mourinho is an admirer of the Hammers midfielder and wants to sign him for Manchester United. In addition to this, the player has refused to rule out a return to Marseille.
Despite his ambition to play in Europe's elite club competition, Payet has suggested that he will not push for a transfer in the upcoming window.
"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 that today's situation does not suit me. I will ask the questions at the right time," he noted.