Madrid know that bringing a top level goalkeeper will not come cheap, but they're not willing to pay more than 60 million euros for Alisson, who is one of several signings they want to close.
Alisson will star in this year's World Cup as Brazil's No.1, pipping Manchester City ace Ederson to the post. He is not anxious about the competition with Keylor Navas and thinks that the style of play of Real Madrid adapts to the way he plays.
According to Spanish newspaper AS, talks between Real Madrid and Roma are now at an advanced stage.
Roma have allowed Alisson's agent Jose Maria Neis to speak to Madrid officials and a £61million fee could be agreed.
Speaking to ESPN, Gab Marcotti said: "I think there is contract negotiation going on [between Roma and Alisson]".
Real are the Brazilian's priority, which means that Los Blancos have the advantage in the race to sign him, although they too won't wait for long either.
The French global appeared poised to finalise a move to Anfield prior to jetting off to the World Cup in Russian Federation, with a picture of him in the club's kit leaked online.
The player was said to be keen on seeing his future resolved before the World Cup starts.
"We'll see if anything happens this week". It does not necessarily represent the position of Liverpool Football Club.