In fact, what "reactive programming" does is solve the problem that FP has with reactive systems[1], in that it isn't suited for them at all. FP, pretty much by definition, is suitable for transformational systems, i.e. systems that map some inputs to some outputs and are then done.
With just FP, there really isn't any way to build reactive systems, that is systems that continuously react to external and internal stimuli, whereas reacting (responding) to stimuli (messages) is pretty much the definition of OO.
By treating input as (infinite) streams of data and applying collection processing to those, you can sort of map this to the aforementioned dataflow programming and solve your problem. Of course, just using dataflow programming directly is both simpler and faster, but hey...
[1] https://www.inf.ed.ac.uk/teaching/courses/seoc/2005_2006/res...