Liverpool plan to offer Alisson Becker a new contract this summer.
The Mirror says the Brazilian's international team-mate Fabinho will also open discussions over a new contract.
He has had a season which has seen him as the club's most consistent performer during what was an injury-blighted year. Fabinho is about to enter the final two years of his contract.
Liverpool have an option on an extra year with Alisson's contract, which would mean he still has three years left to run, but the club want to reward his excellence with an improved deal.
Reds boss Jurgen Klopp wants to tie down the key pair to long-term deals and the club will respond with negotiations over new deals during the off-season break.
