The Reds have not secured a top-five finish since 2009 and Shearer, who scored 260 top-flight goals during 14 years with Blackburn Rovers and Newcastle United, believes that they are unlikely to buck that trend this season.
"The Kop might not want to hear it but the best their club can hope for this year is fourth place," Shearer wrote in The Sun.
"That's a long shot too. They are in a five-way battle to bring Champions League football back to Anfield.
"It's 22 years since the Reds last lifted the title and I just don't see that drought ending this year. Or next. They are not just going to become contenders again overnight."
Liverpool visit Hearts on Thursday night in the Europa League, aiming to atone for Saturday's 3-0 thrashing at the hands of West Bromwich Albion.