I think Rodgers would be stupid to take the job. With his Liverpool connections and the general mentality of utd fans he would not get a chance imo. They are seething and want instant gratification, they also seem to believe only the very best is good enough for them. Ten Haag is even a split decision with them currently so they won't have an ounce of patience for Rodgers to put his stamp on things.
Honestly i think most managers who would do a job for them won't get a look in because of their fanbase and those who would would be on borrowed time from the get-go. An ex Liverpool manager? he would be lucky to be afforded a 10th of the good will and grace time should they not immediately be battering everyone 7-0.
They are their own worst enemies in many ways, and i like that.