Hard to say. No savings is a bit of a problem because buying (and maintaining) a home does cost money. Typically you need at least 3-3.5% down, plus money for closing costs, inspection, appraisal, etc. There may be down payment assistance programs in your area. And you may be able to negotiate and get the seller to pay your closing costs. But inspection ($300-400) and appraisal ($400-500) is your expense.
You need to sit down with a local lender who can review all of your information. The lender is going to look at credit scores, job/income history, debt to income ratios, etc.
I'm a huge advocate of home ownership; however, I worry about people wanting to buy who have no money. Besides the cost to buy, there is additional financial responsibility in owning and maintaining a home. You no longer can call the landlord when the furnace goes out or your pipes freeze.
If owning a home is your goal, then make it happen! Good luck and Happy New Year!