Neither Loris Karius nor Simon Mignolet, Liverpool's current two goalkeepers, have made the number one spot at the club their own - with manager Jurgen Klopp alternating between the two all season.
His patience for the problem position may be at an end as he is reportedly hunting for a permanent solution for next season.
Brazilian keeper Alisson has been highly impressive in Serie A and the UEFA Champions League this season, keeping 13 clean sheets, but he is no cheap option - Roma apparently value him at €70 million ($110m).
Roma's director of sport, Monchi, yesterday admitted they didn't charge Liverpool enough for the transfer of Mohamed Salah, so the Reds are unlikely to score a bargain this time around.
€70 million would be a world record for a goalkeeper, but Liverpool are keen to get a deal done early as his price could go even higher if he impresses for Brazil at the FIFA World Cup in Russia.
Alisson is Brazil's first choice keeper ahead of Manchester City's Ederson.
