Il Tempo says Liverpool have already made a bid for the 25-year-old.
It is not said how much the offer was, but Roma have reportedly knocked back the Reds' attempts to sign him.
“I am happy in Rome,' Alisson said.
“It's always a pleasure to feel that lots of people are monitoring you but my head is focused on Roma. I leave my future in the hands of God.
“In June, maybe we will speak about it again but for now I am concentrated on Roma.
“Together with my teammates, we have done a great job to not allow the loss of [Wojciech] Szczesny to be felt by the fans.
“I have worked very hard and want to continue along that track."