I know these bank owned properties/transactions can be really confusing and tricky!! I'm going to try to help.
So, how do you know there's an offer in consideration by the bank? Did you talk to an agent who is listing the property?? Because, what will tell the tale is whether or not the offer has been agreed to by the bank/seller or not. If the offer is just there and not been responded to by the bank, then you might have a shot at submitting a competing offer. If it's been signed off on by the bank and the bank and the buyer have agreed to all their terms, it might be too late for you to submit anything.
IF the bank has NOT signed off on the offer currently in play, that's up to them as to whether or not they will entertain any other offers. BUT, also know that agents are bound by their licensure to submit any and all offers, and up to the seller as to how they want to respond. That is, of course, if they have not already agreed in writing to accept another buyer's offer. Make sense??
Good luck, Jeff!