Reports out of Germany on Monday report that Portuguese worldwide midfielder Renato Sanches is set to join Milan from Bayern Munich.
Having confirmed the signing of Real Madrid's Colombian midfielder Rodríguez last week, Bayern are looking elsewhere in the transfer market as they hope to retain the Bundesliga title next season, as well as provide a significant threat in the Champions League.
"I can confirm that Milan have shown interest in Renato Sanches, but there is no agreement yet", Rummenigge told German paper Bild.
Portuguese newspaper Record speculated that Milan could take the 29-year-old on an initial two-year loan deal, featuring the option to buy for €47 million. 'But we did not get any further.
AC Milan interested in Bayern Munich's Renato Sanches - CEO Rummenigge
He made just six starts in the Bundesliga and even dropped to Portugal's Under-21 squad despite playing a key role in their triumphant Euro 2016 campaign.
Rummenigge also commented on reports that Bayern would be reigniting their interest in Arsenal star Alexis Sánchez.
"I have the impression that AC Milan is not ready to meet our economic demands, and as long (as that continues) nothing will be done". At €48million (£42m) I would not be dissatisfied'.
And Rummenigge has admitted that Milan - who have already signed the likes of Leonardo Bonucci, Ricardo Rodriguez and Lucas Biglia in an astonishing summer - are interested in him.
Sanches turned down Manchester United to join Bayern.
Ander Herrera commits himself to Manchester United future
United pursued a deal for Real Madrid striker Morata for weeks, before eventually settling on signing Romelu Lukaku from Everton . But, Manchester United hijacked Chelsea's move for Romelu Lukaku and the Blues are now being linked with three major strikers.