The Sao Paolo midfielder has been chased by the Blues since the January transfer window and is tipped to leave South America this summer.
However, Nerazzurri boss Andrea Stramaccioni has now declared his interest in the 19-year-old, who has made 11 appearances for Brazil.
"He is a world-class player," the Italian told Corriere dello Sport. "For me he is one of the most interesting talents on the transfer market today and would be great for us."
Moura made his debut for Brazil against Scotland at the Emirates Stadium in March 2011.