He told reporters after a 3-0 friendly victory over Austria: "I believe and I hope that everything will be resolved before the start of the World Cup".
'If it's not resolved before the World Cup, then it will be discussed after it because my head will be focused only on Brazil.
The Reds want to sign Alisson this summer but it seems Roma are determined to retain his services, throwing Liverpool's chances into doubt.
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He will start for Brazil at this summer's World Cup in Russian Federation, but before that kicks off he wants a deal wrapped up.
He is very happy with Roma and the transfer rumours are just rumours.
"There are options that we are working on, together with Roma and with respect for my club", he told Globoesporte.
But Alisson's representative has also been in talks with a number of other clubs across the continent, although only Real Madrid and Chelsea have been identified as teams who are also in contact with the 25-year-old.
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They have been linked with David de Gea and Thibaut Courtois as well as Alisson.
Alisson kept 22 clean sheets in his 47 appearances for Roma last season, with the Giallorossi reaching the Champions League semi-final stage. The truth is that I left everything in the hands of my manager.
"If it's not before the first game, it will be after the World Cup, that's my thinking 100 percent", Alisson continued.
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Even for a player that has grown up in the spotlight, the past week must have felt intense for the 23-year-old. But the goals will come, and I am sure of that".