Also, getting involved in any food-related business is not something to be taken lightly. It's very time and capital-intensive, so be sure to put together a well-thought-out business plan.
While a landlord may be willing to rent part of a parking area, you are then faced with the issue that you have no physical building in which to house your food market.
So what are you planning to do? Build a building on the premises? Doing so will require the landlord's permission, possible zoning challenges, construction permits and a fair amount of money. Did I mention that this kind of business is capital-intensive?
Set up small stalls? You'll need insurance to cover pedestrians as well as any food-related illnesses that could arise. Most importantly, do your research carefully. There may be a demographic or financial reason that there is no food market in that area.
It may be that the area is not well served by food distribution channels. Or, that nearby residents are not particularly interested in a food market.