Sanches moved to the Bundesliga club from Benfica last summer, having been linked with a host of elite European clubs.
As a result, he has been tipped to make a move away from the club this summer, even if it is on loan. Sanches won the award for best young player of the tournament and joined Bayern Munich for an initial £30m.
Sanches arrived in Germany to great fanfare last season, fresh from Portugal's success at UEFA Euro 2016.
Sanches couldn't break into Bayern's team.
However, they seem to be actively working on Bayern Munich flop Renato Sanches as well, and it appears that the Portuguese pearl could be on his way to Italy this week.More news: Geale: Mayweather-McGregor Hype is 10 Times Better Than Fight
According to Four Four Two, Milan wanted to take the player on a two-year loan, with an option to sign him at the end of the deal for £35m.
"But we did not get any further".
Rummenigge also commented on reports that Bayern would be reigniting their interest in Arsenal star Alexis Sánchez.
I have the impression that AC Milan are not ready to meet our economic demands, and as long as (that is the case) nothing will be done. At €48million (£42m) I would not be dissatisfied'.
The Rossoneri have stunned world football landing Leonardo Bonucci from Juventus, while Milan have signed defenders Ricardo Rodriguez, Andrea Conti and Mateo Musacchio, midfielders Franck Kessie, Lucas Biglia and Hakan Calhanoglu, and forwards Andre Silva and Fabio Borini.