Ibrox side Glasgow Rangers look poised to get shot of their £1.8m signing.
Herald Scotland reported this week that the 29-year-old is on the brink of clinching a move to the Championship club.
Garner joined Rangers for £1.8 million last summer (via The Record) but only managed seven goals in 31 Scottish Premiership appearances.
It was his second underwhelming season in the goalscoring stakes, having only struck six goals in 39 Championship matches for Preston North End throughout the 2015-16 campaign.
The Rangers man netted 46 goals across two League One seasons with Preston but it is clear that he struggled with the step-up in class to the second tier.
And Lawrenson, a fan of the Lilywhites, gives him credit for his industry, but the BBC pundit question whether he will do the business in regards to scoring goals.
"I’ve seen him play so many times for Preston, with them being my club,” he told The East Anglian Daily Times.
"I’ll tell you now, he’ll be one of the hardest working centre-forwards that Ipswich Town fans have seen in the club’s entire history. He’s a nuisance, an absolute nuisance for centre defenders – they absolutely hate playing against him.
"The only problem with Joe is that he doesn’t score enough goals. Don’t get me wrong, he scored a lot of goals in League One and will get goals in the Championship, but he’s not prolific."
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