Mundo Deportivo says Barca are turning to Leao after being frustrated in their pursuit of Athletic Bilbao attacker Nico Williams.
Milan are prepared to sell Leao this month for €90 million.
Barcelona president Joan Laporta really likes Leão and a serious attempt to get a deal done will be made.
Leão has scored 58 goals and 50 assists in 211 competitive games for Milan.