I go the opposite way on my mtb to get from Levenshulme to Roman Lakes and there’s quite a few off road routes.
Here is a very rough description! You can firm it up by googling Manchester Werneth Low MTB and looking at the end of the loops of the Garmin/Strava posts which this route is based on..
Best to go through Brabyns over the canal aqueduct along the canal and turn left off to Chadkirk Chapel, which brings you out by Otterspool Wier then there’s a bridleway along the Goyt all the way to Bredbury. Take a short road hop to Pear Mill (there is a shortcut which takes you to Vernon Park) then turn right under the M60 left at the top of the track through to Brinnington and into Reddish Vale.
From north end of Reddish Vale you climb out past the school and down the road to Levy. There’s a right turn which will take you on to the Fallowfield Loop.
Follow the Loop until Debdale Park and turn left along another bridleway which takes you to the Ashton Canal and National Cycling Centre. From there you can follow the canal past City’s ground into town.
It will take a bit of time, but there’s very little road and it’s not as complicated as it sounds….