Sure, you can offer anything that you want. The bank has an idea of what they want, and they may not consider your offer. The nice thing about a bank is that you don't need to worry about hurting their feelings. However, if the competition is stiff, you may be outbid by another party.
If the bank is asking more than what a property is worth, you might consider lowering your offer if an offer is rejected and several weeks pass and the property is still on the market.