Liverpool boss Klopp pulled off a major transfer coup earlier this month, forking out £66million to sign Alisson from Roma.
The Brazil international, who impressed as his country reached the World Cup quarter-finals in Russia, has been signed to replace Karius.
Karius has endured a rocky few months, making two mistakes in the Champions League final defeat to Real Madrid in May before suffering a dire pre-season.
And Globo Esporte claim Liverpool boss Klopp told Alisson information about Karius prior to the goalkeeper’s arrival.
It is said he talked extensively with Alisson, with contact between both parties starting back in January.
That was before Karius propelled himself into the spotlight with two huge errors on the biggest stage of European football.
Globo Esporte say the Liverpool boss assured Alisson of a starting role, informing him he would be above Karius in the pecking order.
And that helped persuade the 25-year-old to reject Chelsea and Real Madrid.
Real were initially frontrunners to sign Alisson but the La Liga giants flatly refused to meet Roma’s asking price.
Chelsea were interested too but, despite bidding £53m, ultimately lost out.
Klopp, meanwhile, has told Liverpool fans they will get their first glimpse of Alisson when they face Napoli on Saturday August 4.
He said: “Obviously he is a world-class goalkeeper, so we are not going to say ‘let’s have a look’. He will play, of course.
“When Alisson is ready, he will be in our goal. We all need to help him so he can perform as good as possible.
“He is desperate to play. He could have joined us here in America but it made absolutely no sense.
“He had a long year and, as Brazil’s No 1, it was quite an intense year, so I sent him on holiday again. There will still be two games to play and West Ham is only the first game of the season, not the last one.
“I would say he plays in Dublin [against Napoli].”
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