According to the Mirror's David Anderson and Adrian Kajumba, the Reds started the bidding for the Brazilian on Tuesday with a £62 million offer, moving themselves into pole position. Roma are believed to want at least £66 million for the stopper.
If the Blues land Alisson, it will open the door for Real Madrid to swoop in and land Thibaut Courtois, who has just one year left on his contract.
Per the report, the Blues and Real have already held talks regarding the Belgian, and the Premier League side are willing to cash in, rather than lose him for free next summer.
As shared by Oliver Bond of Anfield HQ, The Times reported Liverpool feared a scenario in which Chelsea swept in for Alisson, similar to how they beat Manchester City to the signing of Jorginho:
The Mirror also stated Roma feel "short-changed" by Liverpool after Mohamed Salah made the move to Anfield last summer, but the Reds are confident.
For manager Jurgen Klopp, finding a solution to the club's goalkeeping woes has to be a priority this summer. Current starter Loris Karius made two major mistakes in the UEFA Champions League final, a 3-1 loss against Real Madrid, and fans have completely lost their faith in him.
Simon Mignolet likely also isn't the solution, as the Belgian was unable to beat out Karius for the top spot last season.
Chelsea's need would be just as big if they lost Courtois. But according to Sky's Kaveh Solhekol, they have other options if that deals falls through:
The Alisson deal will set a new standard for goalkeepers if his valuation is met, highlighting his remarkable rise. The former Internacional stopper wasn't even Roma's regular starter a year ago, as he spent the 2016-17 campaign as the back-up to former Arsenal man Wojciech Szczesny.
The latter left for Juventus last summer, opening the door for Alisson to become the superstar he is today. The 25-year-old grabbed it, usurping Manchester City's Ederson as Brazil's starter along the way.