Of course you can leave somebody the proceeds of sale. All you have to do is direct in your will that the house be sold and the proceeds be paid to X. You should make it clear if it is the proceeds after selling expenses (and possibly the clearing of any loans charged on the house) or the gross proceeds. The executor takes control of the situation, and has considerable discretion over how things are handled. Any costs associated with the house between date of death and the sale of the house, such as heating it to ensure that it does not deteriorate, are a charge on the estate. It is also possible to provide an amount out of the estate to fix up the house to make it more saleable.
It can be a little more complicated if somebody is living in the house.
It can be messy if the house does not sell for a reasonable price. For that reason, it might be a better idea to leave the house to the intended beneficiary.