The duo may find it hard to adapt to Klopp's high pressing, high energy game.
The duo are currently out injured and missed the German’s first game in charge on Saturday, a 0-0 draw with Tottenham at White Hart Lane.
The German’s famous high pressing game was in evidence from the start in his debut game, with young striker Divock Origi posting impressive numbers when it came to sprinting and distance covered as he led the line.
And Carragher says Sturridge and Benteke must buy into that philosophy or they could face exits from Liverpool in future.
“The challenge is that Liverpool are not scoring goals,” he told Sky Sports.
“Can Klopp get Sturridge and Benteke to buy into that? Five or six Liverpool players covered more distance than they've ever done in that game. That's not to say he'll put Sturridge on the bench, but he'll expect it to come. And they'll have to, if they want to stay at Liverpool under Jurgen Klopp.”
Of the two players, it is arguably Sturridge that is likely to adapt to Klopp’s high pressing, high intensity football the best as his game is more naturally suited to it.
However, with his injury record showing that he is highly susceptible to picking up injuries fans would worry that putting in the extra effort Klopp demands could see him spending even more time on the treatment table.
While Sturridge could adapt, Benteke arguably faces a fight to do so, with him being at his best when he is attacking crosses and dominating defenders in the air, something which does not require a lot of running.
For now, both will be hoping that they can just get fit and try to impress their new manager.