If a non-Jewish agent wants to show a property that I own on Shabbos is he allowed to do that? There would be no work performed. The agent is going into the house with a client looking and then they discuss. The buyer may make an offer or may not.
The agent is allowed to show the property to potential customers, if a couple of conditions are met. Firstly when he is hired he was given the freedom to show the property whenever he would like, and not that he is compelled to show it to people on shabbos. Secondly, although he is allowed to do it because it is considered his private job, and not like he is working for you specifically on shabbos, however since he is doing the work on your property, you have to protest his working there. This is done by telling him that you don’t want him showing the property to people on your Sabbath, and after that even if he does show it to people, it is fine. (Obviously you told tell him that). The above would apply even if you presently live in the property. In the event that the agent would be told specifically to sell it on shabbos then I would not be permitted.
O:CH 244-1, M:B 276-11.