the simple answer to your question is that the seller/owner has NO obligation whatsoever to notify the bank that they have received an offer. in typical (more on this later) short sale situations, banks DO NOT review offers since they do not own the property. the bank is not considered a principal or party to the transaction. the seller and seller's agent negotiate the offer as in any normal situation and if an agreement/contract is reached, it is contingent/subject to the sellers' bank(s) approval, then submitted to the sellers' bank(s) to see if they will accept the "short" net proceeds of the sale after normal expenses are covered. the bank can approve, counter or reject the sale or any of the expenses involved.
ok, now the explanation for a "non typical" short sale for which the above does not apply....if an owner has been in touch with the bank prior to the short sale and the bank has pre-approved the owner for a short sale in a written agreement with a preapproved listing price by the bank, the bank will probably want to know about all offers and may suggest that you sign and forward any offer you get for their review. in these cases I suggest you (if you are a seller) have this conversation with the lender regarding any offers you might receive ahead of time and follow their suggestions/direction