The Bild podcast Bayern Insider first reported that City have tabled a new deal for Gvardiol, whose current contract runs until June 2028. Gvardiol himself is understood to be open to a move to Munich, having previously worked with Bayern Munich sporting director Max Eberl at RB Leipzig.
German football legend Lothar Matthäus confirmed on Sky Germany that Bayern have made preliminary inquiries.
"I have a player in mind and I have heard that sounding out is already happening — a former Bundesliga player from Leipzig, currently at City, left-back, can also play in the centre," Matthäus said.
The financial gap between the clubs is significant. City paid around €90 million for Gvardiol when they signed him from Leipzig in the summer of 2023, and they are expected to demand a similar figure to sanction any sale. Bayern, who won the Bundesliga title again this season under Vincent Kompany, would need to raise funds through player sales first — with Kim Min-jae or Hiroki Ito among those potentially departing — before committing to a bid of that scale.
Gvardiol, 24, has been restricted to a rotational role this season after suffering a serious shin fracture that kept him sidelined for several months. He made 28 appearances across all competitions before the injury. His versatility as both a centre-back and left-back remains highly valued by the club, and City's sporting director Hugo Viana is keen to retain him long-term.
Pep Guardiola, who leaves the club this summer, previously said he would love Gvardiol to stay.
The World Cup in North America begins in June, and Gvardiol is in Croatia's squad. Any final resolution is unlikely until after the tournament.