It very much depends which direction you're coming from Katey as Deansgate is a bit of a nightmare for cars since the cycle lanes have been introduced.
However, once you do get to Deansgate - with the entrance to the walk accessed via Deansgate metro stop - there are quite a few car parks within walking distance (the nearest being on Bridgewater Street just off Deansgate or the NCP opposite the Bridgewater Hall on Albion street) as well as on road parking (with meters) on Whitworth Street west and also nearby Liverpool road, with a couple of parking bays near the Oxnoble inn on Liverpool road.
If you're unfamiliar with the area, it's a great district to explore - Castlefields, Museum of Science & Industry, new Campfield market on a Saturday - plus very many yummy bakery/coffee shops/eateries all around Deansgate when you need to refuel after your walk.
Hope you have a fab day.