The Anfield outfit have been deeply entrenched in their search for a new keeper following Loris Karius' nightmare performance in the Champions League final, whereas Los Blancos are eager to upgrade on their current number one Keylor Navas.
With a common objective of pursuing one of football's rising stars, Roma's Alisson was identified by both clubs as the man to rectify their goalkeeping woes.
While there have been suggestions that the Reds had offered the 25-year-old a contract, according to Gianluca Di Marzio Real Madrid have gone one step further after coming to an agreement with the Brazilian.
The report claims that an opening offer of £44m from Liverpool - plus bonuses - was swiftly rejected and having failing to come back to the table with a counter offer the Spanish giants have jumped ahead in the race after making contact with both Roma and Alisson's representatives.
Alisson is off to Real Madrid, indicates all you need to know about his quality. Top top keeper and I stand by the fact I'd splash out for him— Indigo 🉐 (@IndigoLFC) June 13, 2018
It is understood that an initial offer of £48m was made by Real, which continues to be well away from the Italian outfits valuation of £70m, but after showing a willingness to reach an agreement the deal has swung in their favour.
Real president Florentino Perez, however, is eager to secure the 25-year-old by any means necessary and it is being said that an improved offer of £52m - plus bonuses - could result in a breakthrough in negotiations next week.
Los Blancos are also known to be considering Chelsea's Thibaut Courtois after seeing Manchester United's David de Gea sign an extended contract at Old Trafford, however an informal approach from Real was rebuffed by the Blues.
Liverpool on the other hand have turned to Lazio's €30m-rated stopper Thomas Strakosha after impressing with the Serie A side in the last two seasons, with Jack Butland also remaining a contender to rectify a problem position for Jurgen Klopp.