If this is a bank owned home they may not want that as they will not repair anything as the property is typically sold as is.
But in general going into an agreement without knowing the results of a home inspection is not a good way to go. There could be countless things hidden from the naked eye that could cost you thousands when you move in to repair.
I would submit a contingency removal form that states subject to addendum where you ask for price reduction.
Bank is unlikely to agree but it probably will not hurt to ask.
Do you have an agent?
This is really something your agent should know how to handle.
Remember one thing, time is money. Both agents along with the lender don't need practice writing offers and everyone is working towards the same common goal, and that's closing escrow. If you found damage that was unknown prior to making an offer, if it's an issue with you, it's probably going to be an issue if they have to find a new buyer too.
You might want your agent to extend the contingency period. But with that said, you have every right to ask for repairs after getting the inspection. I'm taking it you bought an REO, bank owned property. The bank will do one of three things. Reject your credit, agree to the credit, or counter you back.
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It's hard to tell from your question whether you've completed your investigations on the property. Do you have an inspection that shows problems? Have those problems been clearly quantified for you?
Your agent should be able to negotiate on your behalf with the seller's agent, and the results of the conversations between the listing agent and the bank will be able to give you some indication of the bank's position. If all parties are aware of the issues, there's usually a way to work it out, even if it means a written request to extend the contingency period.
If you're uncertain about the condition of the property, or haven't received the results of your investigations, you might be taking a risk accepting the property without that information.
I hope this helps.
Offer a lower price, but keep your financial security by keeping this clause in the contract.