Sturridge has once again struggled with injury and fitness concerns at Liverpool this season.
The England striker started just three Premier League games in 2017 but two of those were in the final two matches of the season against West Ham and Middlesbrough, where he impressed.
But Parlour thinks Klopp needs a striker he can rely on and Sturridge is not that player.
"I can't see him having a future at Liverpool," the Arsenal legend said on talkSPORT.
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Who is Jurgen Klopp tipped to sign this summer?
Jurgen Klopp needs to bring a new striker to Liverpool according to Ray Parlour
I can't see Daniel Sturridge having a future at Liverpool
Ray Parlour on Liverpool star Daniel Sturridge
"That's the position that they really need to look at Liverpool in this transfer window, centre-forward.
"Get that real focal player who can hold the ball up, you've got excellent little players behind them, we know that.
"You have (Philippe) Coutinho, (Adam) Lallana, (Roberto) Firmino, excellent players, (Sadio) Mane as well, he's been out injured.
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"I think forward is going to be the most important and I think Jurgen Klopp is going to need someone who will be reliable, play week in, week out.
Daniel Sturridge has not got a future at Liverpool according to Ray Parlour
"A little bit like Harry Kane, I know he missed a few spells but that was just bad luck for Harry.
"Someone who's not going to get those niggly injuries and I think Daniel Sturridge will be on the move.
"A lot of clubs will be interested in him. West Ham for Daniel Sturridge?"