If my parents pay me to help take care of them, can they deduct it as an expense on their taxes?

I have elderly parents with multiple health issues, although both are still ambulatory and who do not require skilled care or personal care (such as bathing and dressing). So they do not qualify for federal or state aid - and besides, they have too much money.
They want to pay me to come over and help them, and I would be willing, but first I need to find out: can they deduct what they pay me from their taxable income? Or could they maybe itemize it as a medical expense?
Thanks in advance!