I believe it is possible. Although banks are way more conservative these days, there are still loans available like their were at the height of the market. They are just more difficult to get, requiring higher FICO scores & much larger down payments.
I am not a loan broker and I suggest you speak with one, my lender has been in the biz 30yrs, you can send her an email, she is usually quick to respond: ASpellman@StratisFinancial.com (Arlene Spellman)
The keywords you want to ask her about are "NO DOC / LOW DOC loans" Also "NO INCOME VERIFICATION OR ASSET VERIFICATION LOANS"
Again, these loans still do exist, but you're going to be bringing in a Hefty down payment, maybe as high as 30%. I am unsure about FICO score minimum, just ask Arlene about it.