Klopp’s Reds stormed to their first title in 30 years last season, winning 32 of their 38 matches to finish an impressive 18 points clear of second-placed Manchester City.
With the Liverpool squad staying more or less the same – and even being bolstered by the signings of Diogo Jota and Thiago Alcantara – the club were expected to at least challenge for the title again this season.
Klopp’s side went top of the table in December but the Reds have since suffered a shocking run of form to slip to eighth, 22 points adrift of leaders Man City.
Even more worryingly, Liverpool have lost their last six matches at home and Hamann believes the Anfield board will be questioning whether a change is needed.
‘I think he will come under pressure from the fans now,’ Hamann, who won the Champions League and two FA Cups at Liverpool, told Stadium Astro.
‘They’ve lost six games in a row [at home], there’s a good chance we don’t see Champions League football at Anfield next season.
‘We know about the financial pressure clubs are facing. The owners said during the January transfer window they can’t spend an awful lot of money so if they miss out on the Champions League we might not seen too many, if any, new players.
‘I don’t know what the manager thinks about that. Will he just compete for a top-four spot next season? Is that enough for him? Or will the club think they need to change things?
‘If [Germany head coach] Joachim Low decides to step down after the Euros, I don’t think it’s a secret that the German Federation would like to have Jurgen Klopp, if he would probably be there first choice.
‘What happens at Liverpool, I do not know. You can’t afford to lose six home games in a row.
‘If they were to miss out on the Champions League, I’m sure questions would be asked within the club. We need to wait and see if the manager has the right answers.
‘I don’t want to look too far ahead and I don’t know what’s happening, but I wouldn’t be too surprised if there was a change made at Liverpool.’
Following the loss, Klopp said: ‘This team is an extreme team. We were extremely successful and now we have an extreme situation as well but we will fight through.’
On Wednesday night, Liverpool face RB Leipzig in the second leg of their last-16 Champions League clash. The Reds won the first leg 2-0.