Rangnick has yet to decide on whether he will join Milan as their technical director or an English-style manager with full control over coaching and recruitment.
Tuttosport claims they are ‘hopeful’ of the Red Bull chief agreeing to the latter but, in the event he does not, he would be entrusted with sourcing a coach.
Assuming Stefano Pioli is on his way out, the newspaper writes Rose is being considered alongside Nagelsmann.
The 43-year-old is well-known to Rangnick, having guided Red Bull Salzburg to consecutive Austrian titles between 2017 and 2019.
He moved to Monchengladbach last summer and has since taken them to third in Bundesliga, only behind Bayern Munich and Borussia Dortmund.
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Source: Football Italia