Payet starred for the Hammers last season, scoring nine goals and creating 12 assists in 30 Premier League games to help them to an impressive seventh-placed finish ahead of the likes of Liverpool and Chelsea.
The 29-year-old midfielder forced himself into the France squad for the European Championship and has continued his form in the tournament, scoring three goals en route to their semi-final showdown with Germany.
Rumours have begun circulating of interest from Chelsea, Manchester City and Paris Saint-Germain, which Bilic feels is natural given the performances Payet has produced over the last 12 months.
"As a club manager, when you have a player involved there is added interest and there is no doubt Dimitri Payet has been one of the stars of the tournament," Bilic wrote in his column for the Daily Mail.
"I understand that with his success, all the speculation about his future will follow. I have even seen one report suggesting I don't want him to do well in case it leads to him leaving West Ham.
"That is not right. I want him to play great. I want him to score a hat-trick and another hat-trick in the final.
"I know then that the giant clubs will come but I would love him to stay at West Ham. We have texted each other over the last three weeks and he is happy at the club. He is our player."