Several injury issues have derailed the 24-year-old’s season as he has just 26 appearances across all competitions under his belt.
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According to Matthaus, Bayern are already laying the groundwork for what would be a blockbuster deal for Gvardiol.
"I have a player in mind and I have heard that inquiries are already being made," Matthaus said on Sky.
"A former Bundesliga player from Leipzig, currently playing for Manchester City, left-back, can also play in the centre. His name is Gvardiol."
Reports have suggested that Man City are keen on securing the defender’s long term future, with his current contract set to expire in 2028.