The Portuguese starlet joined Bayern Munich for € 35 million plus € 35 million in bonuses and although Massimiliano Mirabelli is keen to sing the 20-year-old, the rossoneri are not open to offer Bayern Munich as much as they spent last summer.
Renato Sanches could be on the move this summer. Sanches won the award for best young player of the tournament and joined Bayern Munich for an initial £30m.
Sanches will have added competition for a starting place at Bayern next season.
Staying at Bayern, though, would also mean a battle to make it into the first team.
It feels like Rossoneri are being linked with a player nearly daily, and the latest player to be linked with a move is Bayern Munich midfielder Renato Sanches.
But AC Milan want him on loan for a season with a option to buy permanently for £35m.
"I can confirm that Milan have shown interest in Renato Sanches, but there is no agreement yet", Rummenigge told German paper Bild.
"But we did not get any further". At least I have the impression that AC Milan are not ready to meet our demands. At €48million (£42m) I would not be dissatisfied'.
Backed by Chinese investors, Milan have been busy this summer and have already signed Leonardo Bonucci, Andre Silva, Lucas Biglia, Mateo Musacchio, Ricardo Rodriguez, Hakan Calhanoglu, Andrea Conti, Franck Kessie and Fabio Borini.
AC Milan are likely to face opposition from a number of Premier League clubs, with both Chelsea and Manchester United likely to be alerted by Rummenigge's comments.