The 25-year-old, who is ahead of Manchester City star Ederson in the Brazilian pecking order, has been identified as Liverpools first choice to replace the beleaguered Loris Karius after his Champions League final errors.
However, Roma will demand his release clause of £79million – which is proving a sticking point – while Real have also shown an interest as they look to finally replace Keylor Navas.
And Alisson has spoken about the rumours for the first time and has revealed that an announcement could be made before Brazil kick off their campaign on Sunday June 17.
He told UOL Esporte: I think everything will be resolved before the start of the World Cup, thats what I want.
The truth is that I left everything in the hands of my agent. If everything is not resolved, it will be discussed after the World Cup.
Right now, Im focused only on the World Cup.
There are some possibilities and we are working on all of them, together with Roma, always respecting the club. Well see if anything happens this week.
Only Napoli keeper Pepe Reina kept more clean sheets than Alisson (17) in Serie A last season, and he has earned the No.1 jersey for Brazil at this summers World Cup.
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