Yes, some banks will ask for all of the potential buyers of a particular property to submit their "Highest and Best" offers before looking at any of them.
You do need to be careful and make sure your agent gets good comparable sales for the area so that you can make an informed decision regarding the value of the home. Also, be aware that they will ask for your highest and best offer even if you happen to already be the best.
Robert and Dawn Morris
In my experience with REO properties, the listing agent usually presents all offers to the bank, then the bank either takes the highest, picks one to negotiate with, or asks for highest and best of all buyers submitting offer. All banks have their own protocol, though.