Either figure would be a world record transfer fee for a goalkeeper.
Loris Karius's horror display in Champions League final back in May and perhaps consistent unconvincing displays appear to have forced Liverpool to sign Alisson.
He spoke to Jurgen Klopp yesterday expressing his desire to join the club and Liverpool then increased their offer to reach the agreement.
According to Calciomercato, new Chelsea boss Maurizio Sarri has told Alisson to delay a move to Liverpool - but Sky Italia's Gianluca Di Marzio claims the goalkeeper is set for a medical with the Reds.
Alisson, Brazil's starting goalkeeper, is on Chelsea's radar amid ongoing doubt over Thibaut Courtois' future, although Liverpool are now in pole position to land the Roma keeper.
A sketchy start to pre-season, during which he made one glaring mistake, might have been the final straw for Klopp.
"Klopp opened the door for Sturridge to return to the side, saying after Saturday's goalless draw at Bury that no member of his squad was being ruled out".