Last year's backup goalkeeper, Simon Mignolet, was sold to Belgian side Club Brugge by Liverpool in the summer transfer window, while Loris Karius is on loan at Besiktas and will only return next season.
"Klopp, whose side meet Chelsea in the UEFA Super Cup on Wednesday, told the club's official website: "[It's] Not too cool.
The player to have picked up the problem was goalkeeper Alisson.
The Brazil worldwide came off in the 39th minute of the match after slipping and holding his calf.
Lonergan would provide more experienced cover for Adrián in the short-term, should Alisson miss a longer period of time. Alisson started every Premier League match last season and generates attacking moves with his ability to pass out from the back.
This, meanwhile, has left the Reds paper-thin in the goalkeeping department.
As confirmed by Jurgen Klopp, Andy Lonergan is set to join up with his squad once again.
'He's training only [for] five days or so, catching balls and all that stuff. It looks all good but of course we have to find a solution in the short term and that will be, if nothing happens from now to then, Andy Lonergan'.
'He was in with us. It's a calf injury, which takes him obviously out for a while.
"He was in with us, he's a brilliant character, a really nice lad and helped us a lot in the pre-season, and now we (have) made a decision to work together with him".
"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".
The annual match sees the Champions League winners take on the Europa League victors from the previous season, with some viewing it is as an important game and others claiming it's little more than a glorified friendly.