According to UOL Esporte in Brazil, Liverpool held talks with the representatives of Roma goalkeeper Alisson before he played at Anfield for Brazil.
The Reds have already tied up one summer signing as Monaco's Fabinho will arrive to bolster the midfield, alongside RB Leipzig's Naby Keita, whose move to Anfield finally goes through this summer.
Jurgen Klopp will still be keen on further additions though, and after Loris Karius' nightmare in the Champions League final against Real Madrid last month, a goalkeeper may be the top priority.
A number of shot-stoppers continue to be linked with moves to Anfield, and UOL Esporte in Brazil report that Liverpool are moving ahead with their pursuit of Roma star Alisson.
It's claimed that the Reds held talks with Alisson's representatives on Saturday night, just hours before the goalkeeper played at Anfield in Brazil's friendly against Croatia.
The report notes that Real Madrid remain keen, whilst a deal for the former Internacional man would cost around €70million (£61million), which would make him by far the most expensive goalkeeper of all time.
Alisson, 25, has impressed for Roma since his 2016 move over from Brazil, and he has particularly starred this season, meaning he will start for Brazil at this summer's World Cup in Russia, ahead of Manchester City star Ederson.
Liverpool hope that Sunday's trip to Anfield will be a common occurrence for Alisson next season, and with talks started over the weekend, a big-money bid could be on the cards.