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Published 21:35 11 Aug 2016 BST
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"They have sold Brad Smith to Bournemouth and you need two players for every position so they need someone else alongside Alberto Moreno.
"Milner did a good job against Barcelona but you certainly wouldn't to go into the season without one more recognised left-back."
Carragher also believes his former side are without a first-choice striker as they prepare for their first full season under Klopp as the former defender has revealed that Divock Origi may have eclipsed Daniel Sturridge in the manager's estimations.
"I don't know if Daniel Sturridge will be the starting striker," Carragher continued. "Divock Origi played in a lot of the big games in Europe last season and has done well in pre-season.
"Sadio Mane is a very good signing. He can play in any of the four positions in attack and it looks like he will play on the right for Liverpool.
"They lacked pace and goals from those attacking midfield positions last year but his record suggests he will fix that.
"Roberto Firmino has been praised by Klopp as the player of pre-season and he likes him as a centre-forward, so there's no number one striker at Liverpool."
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