West Ham are braced for interest in their star player this summer, with reports of Chelsea and Real Madrid’s interest already emerging.
Payet has had a wonderful first season in English football, but his reputation is only set to continue to grow if he keeps on impressing at the European Championships.
Payet scored France’s winner in their first game against Romania and also claimed an assist.
Bilic admits that he is expecting interest in Payet to increase in the coming weeks, but he insists that does not mean he wants the 29-year-old to have a quiet tournament.
"Some will say it is a double-edged sword for West Ham, and myself and that if Dimitri continues to play like that, there will be other big clubs circling,” he said.
"I don't think about that though. We are so proud to have him and apart from Luka Modric, or someone else from the Croatia team, I would like nothing better than if he was the player of the tournament.
"After that, what happens, happens but we know he is happy at West Ham.”
West Ham are under no pressure to sell Payet, as he recently signed a new contract with the London club.
West Ham reportedly want at least £60 million to even consider accepting an offer for the former Marseille man.
Payet scored nine goals and created 12 assists in the Premier League during his first season at West Ham.