The former Hoffenheim coach is in advanced talks over an as yet defined role with the Rossonero.
But ex-Inter Milan striker Rummenigge told Gazzetta dello Sport: "In Germany he worked well, he has the advantage of having had two roles, because he was both technical director and also coach.
"Let's say, however, that the thing was not sold in a nice way, because if you have two executives such as (Paolo) Maldini and (Zvonimir) Boban, who were symbols of a great Milan, a more sensitive solution must be found, action must be taken so that it eventually becomes a 'win-win' for the two sides.
"If Rangnick starts like this, it is not a nice way because Boban is already gone and Maldini is against him.
"Will Rangnick be the coach or the technical director? I have no information."