If you know the market value and you are being offered well in excess of it, why bother with the hassle of putting it on the market?
An auctioneer told me recently that he was pitching to an executor for the sale of a house against three competitors. They had all valued the house at around €650k, but he suggested to the executor that he had one client who really wanted to live on the particular road, and if the executor agreed, he would give them an opportunity to buy it for €700k, take it or leave it. The executor agreed and the buyer paid the €700k as they were tired of being outbid.
Brendan