There very well could be. Life in its most basic form, at any rate
Taken from an article on my new favorite website, Wired, scientists believe that water once existed beneath Olympus Mons, a volcano on Mars three times the height of Mount Everest. There may be a chance that the water is still warm, making it very life friendly.
On Earth, it is believed that life began around hydrothermal vents on the ocean floor. So, why not in water channels under a volcano on Mars?
On a side note: Olympus Mons is huge. That’s Hawaii superimposed on top of it for scale. It’s generally believed that there is a hot spot beneath the mountain (same idea as Yellowstone), but the plates on Mars don’t move, so the same volcano keeps getting bigger and bigger.