A bank can decide not to agree to a short sale for any reason. Many, if not most, short sales happen when owners are in default, so that fact alone should not be a basis for their delay.
The general advice above does not constitute an attorney-client relationship: you haven't hired me or given me confidential information by posting on this public forum, and my answer on this public forum does not constitute attorney-client advice.
Unfortunately, it is very much the case that a lender does not need to agree to a short sale. But, now that you've offered to try and net the bank extra money, it is time to determine whether just letting the home go is a safe "business" move for you. Let me know if I can help.
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A bank has no legal responsibility to approve a short sale. A short sale is a request to the bank to ask them to release their lien on the property without being paid in full. This equally applies if you are current on your payments or behind. If you are behind on your payments, then the bank has the right to seek foreclosure.
As the other posting attorneys have mentioned, the real issue is whether or not you are at risk for a deficiency if the bank decides to foreclose. You can work with an Arizona attorney to see if you are insulated from some or all liability from a foreclosure under Arizona's anti-deficiency statute. The reason why this is important is that if you know a foreclosure will not open you up to liability, you have a much better bargaining position with your bank to get them to agree to the short sale. This is particularly helpful if the bank tries to demand that you pay them additional amounts on top of the purchase price.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. I am licensed in Arizona and can only provide general comments on matters outside of Arizona law. Actual legal advice can only be provided after a direct consultation in which all of the relevant facts are considered before providing a response.
The prior answers are on point. My concern is that the person or company handling your short sale simply might not be as skilled as they should be. Many lenders prefer short sales, and if you are getting push back, perhaps it is time to consider bringing in outside assistance. I offer these types of services, and would be happy to chat with you and determine where the snag is at.