"We have received an offer but it is still being studied and evaluated," Barca's board spokesman Toni Freixa was quoted as saying on the club website.
"Obviously, if we were prepared to receive this offer and consider it, it is because there is a possibility we could go through with it."
Bojan, 20, came up through the Barca youth ranks but has found his opportunities limited in the first team. He is currently on duty with the Spanish Under-21s at the European Championships in Denmark.
AS Roma have just appointed former Barcelona B team coach Luis Enrique to lead their side next season.
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