City are yet to lodge an official offer for Gvardiol but have been given encouragement the 21-year-old wants to move to the Etihad this summer and that he is potentially available for the right fee.
RB Leipzig value the highly rated Croatia centre-back at €100 million ($109m) although it is likely that City's first bid will be significantly lower.
"Josko and his advisors have submitted the wish to us for a transfer to Manchester City," RB Leipzig sports director Max Eberl told Leipziger Volksnachrichten newspaper.
"We are in talks with Manchester. There is nothing more to say about it at this moment."
Meanwhile, City are still awaiting formal bids for a number of first-team players before deciding their futures.
Sources have told ESPN that Bayern Munich are monitoring Walker's situation, although City would like him to stay. The 33-year-old has a year left on his contract and the club have not ruled out offering him a new deal.
Both Silva and Laporte are keen to move this summer, but sources have told ESPN that City will not consider transfers unless they receive significant fees.
Both players have deals at Etihad until 2025 and City will demand fees that reflect their contract situations.