The goalkeeper joined up with the Reds squad for the first time on Tuesday at their training camp in France following his transfer from AS Roma last month.
The team will head directly to Ireland from their Evian base this weekend – and Alisson will almost certainly be handed his maiden appearance for the club at the Aviva Stadium.
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Klopp told Liverpoolfc.com: “It’s pretty likely [he’ll make his debut]. We should not waste time.