Alisson pulled up with a hamstring injury in the final minute of injury time in Liverpool's 1-1 draw with Manchester City on Saturday.
The goalkeeper played through the issue for the remaining moments of the game, but Klopp has revealed he will be sidelined for a short period.
That is good news for the Reds though, as they initially feared the injury could keep Alisson out for much longer.
The 31-year-old remains a pivotal part of the furniture at Anfield under Klopp, after arriving from Roma in 2018.
Alisson has kept four clean sheets and made 44 saves in Liverpool's opening 13 Premier League games, as they currently sit third, two points off the top of the table.
Speaking ahead of Liverpool's clash with LASK Linz in the Europa League on Thursday, Klopp said he will not play on Sunday, or during the week after, when there is midweek Premier League matchday.
It will be the fifth successive season where Alisson has picked up a minor setback, and he has done so at an awkward time, given the quantity of fixtures Liverpool will play during December.
Including this evening's clash with LASK, which ended in a 4-0 win, Liverpool will play eight matches up until Boxing Day, and Klopp's side have three huge home games shortly before Christmas.
After the visit of Man United, when Klopp will hope to have Alisson back, Liverpool then face West Ham United in an EFL Cup quarter-final and league leaders Arsenal, so the manager will hope he can be at full-strength.
Caoimhin Kelleher was already set to face LASK, having played in three of Liverpool's four Europa League games so far, but he is now set to deputise in the Premier League too.
The Irishman has only played five Premier League games since joining Liverpool as a 17-year-old, but he could now be thrust in for the next three, as well as their trip to Union Saint-Gilloise in two weeks.
Liverpool face Fulham, Sheffield United and Crystal Palace before their next European outing, and then welcome Man United to Anfield eight days before Christmas.