You don't have to trim the shrubs, cut the lawn and wash the windows to sell a house, but the homeowner who doesn't is telling you they don't care much about maintenance. The same holds true with business sellers.
I agree with Peter and Craig that when a seller puts a business on the market without having at least made an attempt to put together updated financials it's a red flag. It doesn't necessarily mean that the numbers aren't improving, but it does mean that the seller lacks certain common business sense, which is not a good sign from the start.
If you believe the business has significant potential, is undervalued, or otherwise is unique, there are ways to evaluate whether the numbers are truly improving without formal financials.
The first step is to review the bank statements. If revenue is up, that should be reflected in the statements. If it's not, then you can stop the investigation and look for another business.
Even if revenue is up, you still need to evaluate expenses. The bank statements can help with this, but they often won't tell the full story. If you don't have the accounting background to do it yourself, the only true way to get a real picture as to what's going on with the business is to work with an accountant who can help you evaluate the numbers that are available (even if that means building them yourself) and comparing them with the historic numbers and trends.
The problem with this approach is that without recent financials there's nothing current for the seller to make "reps and warranties" to. Those are key components of your purchase agreement where the seller makes specific statements about the financials (and other aspects of the business). If those statements aren't true at the close you can avoid closing and if you find out later they aren't true, you have legal recourse after the sale (all assuming your contract is properly drafted).
The best option in this case may be to ask the seller to prepare financials and hold off on the deal until they do.