It seems things have got serious as the Liverpool Echo are one of several media outlets reporting today that Liverpool have now submitted an official offer for Alisson's signature worth £53m up front with a further £9m coming in performance based add ons.
Roma are considering the bid, a world record for a keeper, but no deal has been agreed and the Italian side are said to want £66m.
The Merseyside team have been looking for a goalkeeper ever since the Champions League Final loss against Real Madrid.
Liverpool reportedly decide to make a bid in the region of £62m for Roma goalkeeper Alisson.
The 25-year-old (1.91m) stands slightly taller than Lloris Karius (1.89m), and while he would have to adjust to the demands of English football, his showings for Roma and Brazil have indicated that he is not afraid of engaging his opponent.
Alisson is the number one choice for the Brazil National team and played in every game for Brazil at the World Cup in Russian Federation. Florentino Pérez's interest in a new goalkeeper is no secret after high profile mistakes by Keylor Navas against Juventus and Bayern Munich last season.
Loris Karius has already made errors in pre-season.
If Alisson does end up joining Liverpool, Roma have a contingency plan - they will put in an offer for Alphonse Areola, who will be competing for a place in the starting XI at PSG with Gianluigi Buffon.