Barkley is expected to be named in the England squad for this summer's tournament, and Osman has backed the 20-year-old to replicate his club form for his country should he be given a spot ahead of other midfielders.
"If he gets the call, I'm absolutely convinced he will do very well," The Telegraph quotes Osman as saying. "He is a level-headed young man and although he is still learning he has shown over the last few weeks what he is capable of producing.
"If he has the belief behind him, who knows what could happen on the bigger stage?"
Barkley has won three caps for England.