The banks will also want the purchase to be resonable so the lenders (who ultimately have to approve the purchase), will be doing a few BPOs (Broker Price Opinion) and/or appraisals to get the market price and go from there before accepting a deal.
The sellers are dropping the price to attract offers so they can start negotiating with the lenders, this does not mean an artifically low, low price will be accepted by the lenders.
You should look at the market value and come in lower than that. If the listing price after so many price drops is already way, way lowr than market price, then I will be careful not to offer too low - the lenders can reject that after you submit the offer and waited for a month or two for accpetance.
In the answer below, what you want to provide is a pre-approval letter not a pre-qualification letter. Ther is a difference in that and pre-approval is more indepth and what you really need when you make an offer.