The Frenchman has been linked to Real Madrid this summer.
The 29-year-old playmaker has enjoyed a quite brilliant first season with the Premier League outfit, scoring 12 times and setting up 14 goals in all competitions as the Irons look on course for a Europa League spot, with Slaven Bilic's side sixth in the table with one match left.
The Frenchman's form has also resulted in a recall at international level as he looks certain to make Didier Deschamps' les Bleus squad for Euro 2016 on home soil this summer.
The drawbacks to playing this well is that you are bound to catch the attention of bigger fish - and Payet has reportedly courted interest from perhaps the biggest fish in the water as Real Madrid plot a move to lure him to the Bernabeu, as reported by talkSPORT.
But left-back Cresswell does not believe that the former Marseille man - who joined the Irons for an estimated £11 million from the Ligue 1 side last summer - will leave West Ham after just one season in East London.
"If you ask Dimi I am sure he would say he has only been here one season and I don't think he will leave. There is no reason to. He loves it here, the fans love him and it is perfect and we are doing well and moving to a new stadium. I know he loves it here and will stay," he said to The Mail.