Liverpool have made a 70million euros (£62m) bid for Roma goalkeeper Alisson, according to reports.
Several British newspapers reported on Tuesday that the Reds had made an offer but that the Serie A outfit wanted 75m euros (£66.5m).
Either figure would be a world record transfer fee for a goalkeeper.
Liverpool did not comment on the matter when contacted by Press Association Sport on Tuesday.
Alisson, 25, has been with Roma since joining from Brazilian side Internacional in 2016 and made 37 Serie A appearances last season.
He played in all five of Brazil's games at this summer's World Cup, keeping three clean sheets.
Liverpool goalkeeper Loris Karius was back in the spotlight last week after a 3-2 friendly win against Tranmere at Prenton Park saw him spill a free-kick which allowed the hosts to score.
Karius was at fault for two of Real Madrid's three goals when they beat Liverpool 3-1 in May's Champions League final, after which it was revealed the 25-year-old German was suffering from concussion.