It is really difficult to give you an answer without knowing the entire situation regarding the property and what other offers have been submitted. I will always speak with the listing agent to try to get an idea of what is needed in the offer for my client to get the deal. Sometimes I will get info and other times the agents are not very cooperative.
The banks are looking for the highest net with a high probability of the deal closing. If you trying to go in with very little down, sometimes a bank will accept a lower offer that has more favorable terms (higher down payment or all cash). They are looking for the highest price, but they also need the deal to close.
If you are not working with an agent or broker, I would be happy to go into much more detail and give you an analysis of the property and to help you determine what you want to do. I work directly with asset management firms and have REO listings, so I do have a pretty good idea of how to structure an offer.
Tony below has his facts straight. The lender wants the best net price, someone with their financing ready to go and is willing to close in the least amount of time possible. As Monique stated, it depends on how badly you want the property.
In our opinion, people can get wooed by a great price and lose site of whether they really like the home.
Best of luck to you,
Mark & Kari Shea
If you wrote your offer with the listing agent, you are doing yourself an injustice. They represent the bank. It doesn't cost you anything to have a buyer's agent, and you will get someone who is strictly on your side.