You can try but I doubt that you will be successful in doing any more than upsetting everyone to the extent that they don't want to deal with you.
Estate agents are employed to get the best price and the owner is likely to take advice from the estate agent. Solicitors tend to more for handling the transfer after the amount has been agreed. If you feel that the price has been set too high, one approach would be to ask the estate agent how many months without a sale before the price will be likely to be reduced. If the estate agent finds another buyer in a few weeks, then you can't have been offering enough. If it's still unsold after a few months, you can go back with your offer.
It is quite possible that the vendor is happy to hold out for the long term rather than accept a really low price.