Speculation has been mounting for some time and has mainly involved the Reds, who are still looking for a top starter after some shaky performances from both Simon Mignolet and Loris Karius.
While there have been plenty of reports a deal could be made, and confidence Roma will sell appears to be high among fans, agent Ze Maria Neis made it clear a transfer is not on Alisson's mind.
"The match against Inter was great. Alisson played fantastically well. Joining a top club? It's too early to say. When a player stands out on the pitch thanks to great performances, there is always a lot of talk. Personally speaking, no club has been in contact yet and he is 100% focused on doing well with Roma. He is happy to be in Rome, and the club is happy with him."
The same article also mentioned Paris Saint-Germain and Real Madrid as possible suitors.
Alisson's awesome showing against Inter didn't go unnoticed on social media, as the 25-year-old put together an excellent performance in the 1-1 draw. He nearly won his team the match with several spectacular saves and also provided the assist for Stephan El Shaarawy's goal.
Here are some of his highlights, via Breaking The Lines:
The Liverpool Echo wondered whether his price tag went up with the great showing:
Roma sit well behind Napoli and Juventus in Serie A and will likely shift their gaze towards UEFA Champions League qualification after the January window closes. Even that could prove tricky, as they're winless in their last four matches in the league.
Their shaky form has led to some belief the club could cash in on some players and start looking at the future, and the duo of Edin Dzeko and Emerson Palmieri are both said to be close to a move to Chelsea, per Simon Jones of MailOnline.
Alisson only completed his move to the Italian capital from Internacional in 2016, however, and it would be a shock to see the Giallorossi move him elsewhere so soon. There's no real replacement in the squad besides Lukasz Skorupski, who lacks the raw talent of his team-mate but has flashed some potential.
A summer move seems more likely, giving Roma the opportunity to push for a strong finish and do their homework on a replacement.
Italy is bursting with young goalkeeping talent―the likes of Mattia Perin and Alex Meret will likely move at the end of the season―and Roma sporting director Monchi is renowned for his ability to find hidden gems.