Kean has rebuilt his career in Florence this season and also broken back into the Italy team under coach Luciano Spalletti.
Tuttosport says Barca chief Deco has taken notice of the striker's re-emergence as he seeks a new centre-forward signing for the summer market.
Juventus striker Dusan Vlahovic has also been offered to Deco, though he is showing stronger interest in Kean.
Kean, who left Juve for Fiorentina last summer, has a contract which carries an affordable €50m buyout clause.