Someone might ask if they can interest you in something when that person is trying to persuade you to buy something or is offering you something.

Can I interest you in our new range of kitchen fittings, madam? 女士，我向您介绍一下我们的新的厨房设备系列好吗？

I don't suppose I can interest you in a quick drink after work, can I? 可以请你下班后小喝一杯吗？