Italian media outlet Gazetto dello Sport, as quoted by The Sun, is reporting that the Reds could agree to a five-year deal with the Brazil worldwide in the next 24 hours.
As is understandable, the majority of supporters are incredibly unhappy with Karius being Liverpool's no.1 and with Simon Mignolet heading for the Anfield exit, the best solution would be to dip into the transfer market for a new gloveman.
It is understood Real Madrid are Alisson's likely destination should he leave Roma this summer.
The Mirror says Klopp is ready to offer his Wales global keeper, who was third choice at the club last season and played just one game, the chance to stake a serious claim for the number one spot at the club.
Liverpool manager Jurgen Klopp appears increasingly unlikely to sign a new goalkeeper this summer to replace Loris Karius, but the Reds could still end up with a new number one in 2018/19 as the boss has been tipped to hand a surprise opportunity to Danny Ward instead.