He scored twice in the Hammers' 3-0 win over West Bromwich Albion on Saturday, leading Bilic to pitch for his inclusion in England manager Roy Hodgson's squad for the June 10-July 10 tournament in France.
"There are no (English) midfielders who are having a better season than he is -- constantly, from the first game at Arsenal," Bilic said. "He's unbelievable.
"Is he a top quality player? Of course he is. Not only because he scored a couple of goals. It's every day, every game, every training session. He is top class."
Bilic, who managed his native country of Croatia before coming to England, said Noble's hard work and team ethic could prove invaluable on the international stage.
"I was an international coach for six years and the national team is not about the 23 best players in one country," Bilic said.
"It's also a team, especially in the big tournaments where they are together for six weeks. It needs stars and lesser stars and all that. Mark is a great person also. He could help England."
England face Russia, Slovakia and Wales in Group B of the 24-team tournament.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
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