Minamino joined Liverpool from Austrian club RB Salzburg in January of last year after the club triggered his £7.25 million release clause.
Lawrenson praised the 26-year-old's work rate, but believes he will continue to struggle for minutes at the club.
“I've never known anyone run so much, he runs everywhere. Sometimes you think with him, just slow down a minute, chew the grass and see what's happening around," Lawrenson said on LFC TV's Preview Show.
“He's got the makings of a top player. Whether he does it here, I am not sure.
“If the worst comes to the worst and they decide that he's not going to make it then we're going to make a lot of money on him."
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