Not really. Imagine a house that was purchased 30 years ago or one that is paid off. The low/no mortgage has nothing to do with the rent.
Your rent should be more about "fair market value".
NOW, what you can coordinate is your rent vs how long your mortgage is.
When I'm paying off my own house, I usually go for 15 years.
For rental houses, I consider a "small business", and I also need to save some of the "profit" (profit = rent minus mortgage)....so I did a 30 year mortgage for my rental in that case. The profit, I sit aside some of it for repairs. And I use some of it for my living expenses of course.
If I have an overage (rare), I can pay a little extra toward the rental mortgage. But that's a better plan for a small-timer-landlord (like me), then a MUST-PAY-EVERY-MONTH higher mortgage payment .. IMHO. (Again, its opinion stuff)
Check craigslist for comparable's.
Other "soft" considerations.
Longer leases. The less number of "flips" I have to do with renters, the easier my life is. I usually give small discount for a longer lease. But INCLUDING CLAUSES (in the lease) that rent can be reconsidered/changed after 3-4 years (<< you don't want to lock in a forever rate).
Again, that's my personal preference as a landlord. I would rather have a 3 year (good) tenant and lose $200-$300 / year vs lots of tenant flipping. Keep in mind, you're probably going to lose 2-4 weeks of rent during the flip process.
Good luck! Most times I'm glad I'm a landlord. A few times a year, it is a complete headache.