The former midfielder does however believe they have a fighting chance of doing just that.
The Reds were hugely disappointing last season as a poor start could not be rectified by their second half form and they finished sixth in the table.
They were also disappointing in the Champions League as they failed to make it out of the group stages, while Besiktas prematurely ended their Europa League run.
They have invested heavily this summer to get back into those Champions League qualification places once again, or perhaps higher, and Hamann says they have a fighting chance of getting there, with Manchester City the team that they are most likely to catch.
“I think they’ve got a fighting chance of finishing in the top four,” he told BreatheSport.
“Will they finish in the top four? I’m not so sure because they were quite some way behind last season. If they catch one team it will be City, I don’t think they will catch the other three.”
Rodgers will stay if they make the top four
Manager Brendan Rodgers came under increased pressure last season as his side struggled, although their second half form somewhat tempered that.
Defeats in both the FA Cup semi final to Aston Villa and Chelsea in the Capital One Cup semi final also saw him become the first manager of the club in 50 years to go without a trophy in their first three seasons.
As well as changing the squad this summer, his backroom team have also been swapped around, and Hamann says they will have to finish in the top four for him to keep his job, while a trophy is also a necessity at some point.
“I think they have to finish in the top four,” he added.
“If Rodgers finishes there then I think he will stay, [but] they have to win a trophy in the next two or three years. A lot will depend on how they start the season and how they finish or where they finish.”