Even if they do agree to lend, chances are the loan would be much more expensive because of your credit history.
Incidentally, the type of loan would be a construction loan. You may wish to read this article: http://www.wikihow.com/Get-a-Construction-Loan-%28US%29
for a better understanding of what these are and the different flavors of these loans.
As ThunderZ said, discussing it with the bank would be your best bet and it wouldn't cost you anything. Make sure you stress that you are not applying at this time, you wish to discuss your options. To assist in that discussion, they will need to know your income, debt load, and, if you have one, a recent copy of your credit report. You can get one free once a year from each of the 3 credit reporting agencies. By timing things properly, you can get a free report 3 times a year: one from each company. With that information, you can discuss options etc. with the bank.
The bank will look at debt to income ratio as well as your credit history. If your debt to income ratio is too high, you will be denied even if you have an excellent credit rating.