La Gazzetta dello Sport claims Milan are set on making Rangnick their man and CEO Ivan Gazidis has made the German director his first priority this summer.
But he talks are allegedly at a standstill and the newspaper claims there are no developments on the proposed contract.
The Professor, as he is called, has been chosen by the leaders at Milanello to lead yet another revolution at the Rossoneri, but the report suggests the tactician is still on standby.
Rangnick has been targeted for an unusual manager role and Red Bull appointed a new Head of Global Soccer earlier this month.
The appointment should have paved the way for the current Head of Sport and Development at Red Bull, Rangnick, to become the manager at San Siro.