It's highly doubtful based on what we know of the environment on Jupiter. Depending on the depth in the atmosphere it goes from frigid space temperatures to thousands of degrees, the atmosphere becomes crushingly high the farther down you go, and the entire planet is highly radioactive. If there actually is life--organisms that can make copies of themselves, grow or divide, consume and metabolize an energy source, etc.--it would be vastly different from any life we know on Earth.
Around Jupiter it's much more likely there is life on its moon Europa. That moon has a very thick crust of ice on top, but with the tidal squeezing and stretching from Jupiter's gravity it warms up enough to maintain a vast liquid ocean under that crust (as determined by geysers of water erupting through cracks in the ice). When you have liquid water and a source of energy, as well as that moon being bombarded over billions of years with the same comets and meteors that brought complex organic molecules to the early Earth, there's a very good chance life could have arisen in that cold ocean. I would love it if we could send a probe there that had a way to drill or melt its way down through the ice to reach that subsurface ocean and send back pictures and videos of what it finds. Life or not, it would be fascinating.