You may come across vendors wishing you to declare a lower price than the price you've actually paid. This is a not unusual (though decreasing) practice in many Mediterranean countries and is all about the vendor having to pay less tax on money received. But there are a number of problems with this. First, although it's widely allowed on a nod and a wink, it is in fact illegal, and you may justifiably be uncomfortable with this.
Secondly, you now have an undervalued property (which could have implications on the price you later receive), and you have sale documents which don't accord with the mortgage documents, which could cause a real headache. And consider - the vendor has avoided a chunk of capital gains tax, but that simply makes your capital gain appear all the bigger when you come to sell the house in years to come: you will be paying the tax they saved! The only way to do this is for you to work the same fiddle with your buyer. In short, you have nothing to gain from this (except possibly a small cut in the actual price you pay) so it's to be avoided.