I don't know about the 'average amount' people would offer below the asking price in any area for any price - it really depends on whether the house is priced competitively or realistically.
If a house is worth $700K, the homeowner priced it at $840K, then offering 20% below asking only brings you to where the house should really be priced at to start with. However, if the house is correctly priced at $700K, then the seller might not be willing to sell you the house for $650K or even $690K.
So, I think the best thing for you to do is to ask your Realtor to provide you with a comparable market analysis tor this home. Only by looking at the houses sold, currently available and the market trend, will you be able to make a reasonable offer that's realistic and beneficial to you.
If you don't have a buyers representation agreement with an agent, you should find an agent in whom you believe you can place your trust. The agent will then be legally able to give the best advice for the situation.
The banks may or may not negotiate on a price. They may stand firm. Expect homes to be sold in AS IS condition, otherwords do not expect the bank to fix things or pay for inspection reports.
If you are serious about purchasing a home, make contact with a Realtor, sit down and discuss your options and what areas are of interest to you.
Average list price: $692,413
Average sold price: $672,463
Hopefully, this information will be helpful. Do let me know if I can be of any other help.