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Published 17:58 5 Apr 2017 BST
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However, the second half of Sturridge's time at Anfield hasn't gone to plan at all.
Over the past three seasons, he has scored just 14 league goals, and has been hampered by injuries.
Jurgen Klopp also doesn't seem too convinced by Sturridge. You get the sense that the Liverpool manager wouldn't fight to keep him if a suitable bid came in.
Carragher, who played alongside Sturridge at Liverpool, reckons the 27-year-old should leave the club in the summer to get his career back on track.
"I don't think Daniel Sturridge has ever been a Jurgen Klopp-type of player," Carragher told Newsweek.
"When everyone has been fit he's never really played. He's got injury problems which is an issue, but I'll probably be surprised if he's there next season.
'It might be better for everyone if he moves on and tries to rejuvenate his career because he had a brilliant start to his Liverpool career - him and [Luis] Suarez were devastating. But it just seems to have tailed off now."
Carragher also backed Sturridge to score goals again if he avoids injury and can find a team to suit him.
"You just hope he can get a really good pre-season behind him and really go in firing, because I think when Daniel Sturridge was at his best two or three years ago I think he was the best English striker out there.
"Now, he's fallen down the pecking order because he hasn't been playing, but if he could get back to those levels, he's right in there in the England team and England squad."
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