Two of them are abundant carbon, nitrogen, oxygen, hydrogen and sulfur and a source of energy that will ensure that there is a continuous flux of compounds that are not very stable so they can take part in chemical reactions to generate complex molecules.
These 2 conditions might exist in the atmosphere of Jupiter, if lightning produces enough unstable molecules.
However, there is a 3rd prerequisite, the existence of inorganic catalysts, e.g. the sulfides of iron, cobalt and nickel. Other transitional metals might also work, but they are much less abundant, so they are unlikely to be used by life in the beginning.
The problem is that on Jupiter rocks with metallic minerals are found only very deep under the exterior part made only of light elements, at depths where the pressure and temperature might be to great for any life form.
So we do not know for sure, but it seems unlikely that life could have appeared on Jupiter or Saturn.
On the other hand, on the large satellites of Saturn and Jupiter, there are much more chances for a place with good conditions to exist, than in any other part of the Solar System besides Earth.
We don't know how those elements interact in high temperature/pressure/dynamic environments. Some compounds which are very stable here may be less so there. Some inorganic form of ice may behave in a very organic way under certain conditions - we just don't know - until we send a probe there.
We haven't observed abiogenesis and experiment/observation is the ultimate guide.
But "current thinking" is that we just don't know. Yeah, it might. Can't prove it either way.
You have to remember just how _big_ Jupiter is. There's a lot of room for different environments and complex interactions. The only problem is it's quite far away and quite hard to get a good look at (especially the "internal" bits).
Wonder if all that ammonia, lightning, water and other things going on might have lead to simple forms of life blowing around in the atmosphere, or if there's simply way too much blowing to allow that to develop? What's the current thinking?