Manchester United could probably have had Pep Guardiola, but in January 2013 the Catalan had agreed to take over at Bayern Munich. Instead, four months later, United appointed David Moyes as Alex Ferguson's successor.
United could also have signed Jurgen Klopp in the summer of 2015, but stayed with Louis van Gaal for another season before Jose Mourinho signed a three-year contract in May 2016.
It is unthinkable that a manager tainted by association with City or Liverpool could ever work at United. Had the club believed Guardiola or Klopp was a good or better candidate then maybe, just maybe, United would be playing with the style associated with the Catalan or the attacking power of Klopp, and Mourinho would be working elsewhere. Right now that is what many United supporters would like — for the Portuguese to leave Old Trafford.