Liverpool are in talks to sign Preston's Davies for £2m as they look to find a solution for their central defensive crisis.
In reaction, Liverpool great and former Preston defender Lawrenson told BBC Sport: "Ben Davies has done well at Preston and has let his contract run down so he was going to move on in the summer. If he'd gone to Celtic, which I'd heard had been agreed, then I was thinking he could do well there, but being honest I didn't really see him as being good enough to be on Liverpool's radar.
"He's a real steady Eddie. He's left-footed and quick enough but he's not got phenomenal pace or anything like that.
"He's been good in the Championship, very good.
"But I've watched him and thought, up against the extra nous and quality you get in the Premier League, on top of extra pace, it will be a test for him. You wouldn't want to just throw him in to face Manchester City next Sunday, put it that way.
"This is obviously a great move for him, I just can't see him getting near the first team. Nat Phillips has done well when he's come in and he is probably a better player.
"So, Davies would be behind him and also Rhys Williams, so even before Joel Matip comes back and the other two long-term injured players - Virgil van Dijk and Joe Gomez - he is going to be below them on the list. And Fabinho and Jordan Henderson too.
"I am not sure he will play very much at Liverpool, but the experience alone should be fabulous. I hope he experiences playing in the first team, but even if he is just sitting on the bench then it is still great for him.
"He has come through the ranks at Preston, learned his trade with loan spells in the lower divisions and improved a lot. He has done really well.
"Regardless of whether he gets a chance or not, it is a great move for him and Ben is a lovely lad. I've got to know him over the years and with people like that, you just think 'great opportunity and good luck to you'."
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