Ask your agent to check with the listing agent to see if there have been other offers and if the bank/seller has countered them, and if so, at what price (net). Some listing agents will not respond to such an inquiry, but others will, so you may or may not be able to find out. But if you can find out, this is good information to have.
A lot of this decision depends on how heart broken you will be if you don't get the house. If you absolutely love the house and will just die if the offer is turned down, then offer close to the asking price. Make sure you insist on an inspection period and find a really good inspector. That will give you some idea of how much it will cost to repair (if repairs are needed). Asking for the bank/seller to pay some of the closing costs, provide a home warranty, and closing within 30 to 45 days (or even sooner) is likely to be something they will agree to, but if you give them a lowball offer, they may turn it down or come back with a counter-offer (which isn't a bad thing). If you offer gets turned down, you can submit another offer, but someone else might also beat you to it.
Since this is spring and we are just now entering into the prime real estate season in Minnesota, banks/sellers are not very likely to agree to a lowball price on a REO that has just been on the market for a month.
That may change later in the year when the season is over (September) and when it has been on the market longer, but right now, they have no incentive to sell for less.
Remember, banks/sellers have had this property evaluated by at least one independent real estate agent who is experienced with BPOs and the cost of the repairs have already been figured into their price. They will have a specific net amount in mind that they need to get for the home and they know they are very likely to receive more than one offer on this home if it is priced right and in decent condition.
If you are using FHA financing, remember that not all REOs will pass their inspection requirements and your agent may need to negotiate with the seller to have some repairs made so that FHA financing can be used. That can affect the likelyhood of the offer being accepted as well.
Good luck and happy hunting!