The Brazil international has left Japan and will miss Liverpool's match against the Yokohama F Marinos at the Nissan Stadium.
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Alisson has been released from the squad for 'personal reasons', says the Daily Mail.
He took no part in Tuesday's training in Yokohama ahead of their latest tour friendly.
Alisson's exit will mean more minutes for summer arrival Giorgi Mamardashvili, who featured in defeat against AC Milan on the weekend.