The Rossoneri had been linked with a move for the German since late last year, and it was expected he would take over as technical director and coach.
It was believed Rangnick was discussing his departure from Red Bull, where he is head of sport and development, in order to take over at Milan at the end of the season.
Milan are unbeaten in their last eight Serie A matches, six of which are wins, and it’s believed Rangnick wasn’t pleased by suggestions he would have to operate solely as technical director with Pioli as coach.
Another deciding factor is Pioli’s contract runs until 2021, meaning the Rossoneri would have had to pay the remainder of his contract while paying for Rangnick’s release.
Instead, it now looks as though Pioli will stay on as coach for the foreseeable future along with Paolo Maldini, who would have left his post as technical director if Rangnick was brought in.