The striker has struggled to make a major impact since joining Glasgow Rangers in the summer.
Garner was one of Mark Warburton's marquee signings during the summer as the Evening Times reports that his move from the Lilywhites cost the Gers £1.8m.
Rangers' Joe Garner
However, the 28-year-old is yet to really justify that price with just three goals coming in his first 10 appearances for the Light Blues. But Mellor suggested that the way he bounced back following the drought at the start of his time at Deepdale should give Rangers fans more than enough confidence about the forward's prospects.
"I can reassure Rangers fans of Joe Garner’s quality," he said, as reported by the Evening Times.
Garner, during his time with Preston
"It took him 18 games before he got his first goal for Preston. As soon as he got going, he adjusted and he settled into life at the club that was him off and running.
"There was pressure because he was a Preston fan growing up and now there is a different pressure going up to Rangers and playing for a huge football club. Once he feels part of it, he will be a huge player for Rangers, but you have to give him time."
One thing that should give Garner hope is the fact that he cost so much in the first place. The fee that brought him to the Scottish Premiership highlights Warburton's belief in him, and should arguably mean that the manager remains determined to give him the amount of opportunities that will eventually allow him to justify the price tag.
And as Mellor highlighted, Garner has previous experience of coming good after a slow start. After joining Preston in January 2013, he had to wait until August the following season to bag his first goal for the club.
And that drought makes his overall record for the side all the more impressive. From the game that saw his first goal onwards, Garner's league record for the club saw him score 49 times in 114 appearances, so he will be hoping that once he gets properly up and running, he can do something similar at Ibrox.