The ex-Huddersfield Giants forward came off with a knee issue during their 48-0 home loss to champions St Helens almost a fortnight ago.
It was a bitter blow for the player, just two games back into action after lockdown and in his first season at Emerald Headingley after joining from their West Yorkshire rivals.
However, Mellor is responding well to treatment after being told the damage was not too serious.
“It’s coming on better than I thought,” he said.
“I went down with my knee thinking it could be the worst scenario.
“I’ve done my medial ligament before which is an eight to 10 week job.
“But when you’re laid there and you’re in so much pain obviously you just have no idea what it is.
“There’s so many thoughts that go through your head when you’re laid on your back so it was quite a relief when they said it’s nowhere near your ACL and it’s not your PCL either.
“It turned out just to be a lateral ligament.
“I tore that with just a Grade Two and my soleus, a muscle in the back of your knee.
“I got told I’d be out for four to six weeks but I’m nearly two weeks in now and my rehab’s going really well.
“I’m not far off running and it’s going better than expected.”
The former Bradford Bulls player has made an impressive start to life in the blue and amber.
Rhinos face Salford Red Devils next Saturday but he has targeted the Catalans Dragons game in Perpignan on Monday September 7 as his comeback.
Mellor, 25, said: “Next week will be too soon so hopefully the Wakefield game but that’s been brought forward a day and every day probably matters to me at the moment.
“If it’s not the Wakey game it will be the Catalans match I’d have thought.
“I’m young and fit and healthy so hopefully I can knock some time off what they’re saying. That’d be nice.”
On the setback, he admitted: “It has been frustrating especially when you’re watching the lads play and seeing them all going out to go training and you’re stuck in the gym doing your rehab. There are some pretty dark places but there are people in a lot worse position who are out for a lot longer so that’s one positive for me – it’s just a short-term thing and then I will be back out there.”
After that nilling by champions Saints, Leeds responded with a better display before falling 28-10 against Wigan Warriors at St Helens on Sunday.
“There was so many positives in that display but so many negatives and I think that was our problem,” explained Mellor.
“The negatives just outweighed the positives a little and cost us in the end. The pleasing thing was we were right in the fight. With 10 minutes to go, the game could have gone either way.
“There was just a couple of pivotal moments that changed it for us. Looking at it as a whole, though, it’s obviously a lot better than the Saints game. Yet we felt in it against Saints – I didn’t feel like we should have been down 24 nil at half-time.
“We put our gloves up and came out with a bit of a fight in us. We were a bit unlucky but the scoreline was a lot closer in that Wigan game and the boys are now building towards getting the result against Salford.”
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Thank you, Laura Collins