The Real Madrid attacker is said to have snubbed the chance to move to Liverpool because he felt they weren't big enough.
With Brendan Rodgers yet to find a replacement for the recently departed Uruguayan, the club have been looking high and wide for a player anywhere near his ability and repute to come to Anfield and carry on the good work that the Northern Irishman has put into place.
But the club have found that sourcing that genuine world class talent is not an easy thing to do, with many of the best forwards in the world already at the biggest, and richest teams in Europe.
Looking at Karim Benzema, Rodgers would have surely have hoped that the promise of first team football would be enough for a player that has plenty of goalscoring potential, but has often struggled to really nail down a first team spot for Los Blancos.
However, amazingly Benzema is reported to have snubbed any interest in joining the historic Merseyside outfit, claiming that they're not a big enough team for him.
Former Ireland striker Aldridge, who starred in a short spell in Spain with Real Sociedad as well as at Anfield, was astounded by the former Lyon forward's claim.
"In my opinion I think he's a decent striker," said Aldridge. "But he can't even get a place for Real - he plays a bit part. With the players that they've got he's not going to get a game.
"It's quite shocking to disrespect a club of Livepool's global stature with those words, we all know Liverpool and Manchester United around the world - they're huge.
"So I don't know where he's coming from there, it's quite strange."
The Liverpool native reasoned that the Reds have had recent success in Europe's premier competition in not so long ago, with Real themselves only just ending a spell with out a Champions League triumph.
"It wasn't too long ago that we won the Champions League," he added.
"You look at the history of Liverpool football club, and there's no bigger or greater club in English football."
Though Benzema's belief about Liverpool show little understanding of the history of English and European football, it is likely Reds fans wouldn't want someone with such an attitude at their club even were he to decide a move was for him.
To put it simply, Karim Benzema may not be big enough for Liverpool football club.