Klopp said the Brazilian will definitely not be available for Wednesday's UEFA Super Cup meeting with Chelsea. Although Klopp played down some of the stories that suggest a lengthy absence, he added the prognosis is not good, per Sam Williams on Liverpool's official website:
"[It's] Not too cool. It's a calf injury which takes him obviously out for a while.
"I don't want to make now [an] exact prognosis on when he will be back but it will not be Wednesday for sure, so now then we have to see. It takes a while, it takes a couple weeks for sure, and we have to see.
"I saw already like 'six weeks' and stuff like this, but Ali was not a lot injured in his career so I would like to wait a little bit to see how he develops in that process now, but he is not in for the next few weeks."
Alisson, 26, enjoyed a superb debut season with Liverpool last term after his £66.8 million move from Roma in July 2018.
He played every minute of Liverpool's Premier League campaign as they finished second by a single point to Manchester City.
He was also ever-present in the Reds' triumphant UEFA Champions League campaign.
His addition to the squad, along with the January 2018 signing of Virgil van Dijk, had a huge impact in turning Liverpool from a shambolic defensive side to the most frugal outfit in the Premier League:
Klopp had almost no need for back-up goalkeeper Simon Mignolet last term.
But after the Belgian's summer exit to Club Brugge, his replacement, Adrian, was called into action just 39 minutes into Liverpool's season opener against the Canaries on Friday:
The European champions were already 3-0 ahead at that point, and Divock Origi added a fourth soon after.
But Adrian now faces at least a few weeks in the side, and Liverpool have some tough games approaching.
Adrian, 32, is a talented and experienced goalkeeper and arguably an improvement on Mignolet as Liverpool's No. 2.
However, given how crucial Alisson was for the Reds last term, his absence will be a big blow as Klopp's side look to make a fast start to the new campaign.