The 34-year-old’s contract at Anfield is set to expire at the end of the season, although talks over a new deal are reportedly underway.
Alisson recently made his desire to remain at the club known, saying: "Yes, I want to stay. I'm focused on playing every game, but in my mind I'm happy to stay.
"It also depends on lots of aspects and different situations. But my will is to stay - I'm happy here and my family is happy too.
"I'm still hungry for titles and delivering good performances. I want to play at the top level for as long as I can."
According to TeamTalk, however, Liverpool are well and truly preparing for life after Alisson and are particularly keen on two Premier League goalkeepers.
Brighton’s Bart Verbruggen is the priority target, but Liverpool are also keeping tabs on Aston Villa’s Zion Suzuki.
Verbruggen is under contract at the Amex Stadium until 2028, so may be more gettable next summer than Suzuki, who only joined Villa last summer.