Hard to tell. He did well there before but, having been at Liverpool meanwhile, he may not fancy what he might see as a step down. Such "homecomings" don't often go well either, though I don't know to what extent that would put him off if he does want the job.
Well, it is very obviously a step down from Liverpool, but it isn't a step down from no job at all. I do think Rodgers may well expect a bigger and better offer to come his way, though. He's not exactly short of self-belief.