The Japan international only moved to Bologna from Sint-Truidense a year ago, but has been a sensation in Italy.
21-year-old Tomiyasu cost €9m when he arrived from Belgium, but the Rossoblù now value him at €20-€25m.
Roma have been pursuing the defensive all-rounder, while Bundesliga side Bayer Leverkusen are also interested.
Paulo Fonseca’s Roma have an excess of right-backs and one would have to leave if they are to sign Tomiyasu.
Bologna want to hold on to Tomiyasu for another year, believing his value will rise even further.
Roma have tried to tempt Bologna into a sale by offering Alessio Riccardi and Juan Jesus in exchange. Their efforts have proven fruitless and a deal is looking remote at the moment.