The Spain international joined the Reds last summer from Sevilla and started brightly, but his season trailed off in the second half of the campaign.
And former defender Lawrenson admits Brendan Rodgers must look to strengthen in that area of the field before the transfer window closes.
He told the Liverpool Echo: "Liverpool need a new left-back. There were some rumours knocking around last week that Barcelona were sniffing around Alberto Moreno.
"I'd be surprised if they want to take the Spaniard, given how, since the New Year, he's been really, really struggling for form.
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Mark Lawrenson says Liverpool need a new left-back
"Moreno started the season well after coming in from Sevilla and scored that fine goal at White Hart Lane, but it all fell apart in the second half of the season.
"Worryingly, quite often he has looked a little boy lost in the big games.
"Moreno deserves another chance. But we need more competition in his position, because it's clear Brendan Rodgers no longer has any real faith in Jose Enrique."
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