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Richards, 22, came through the Reading youth academy and signed his first professional contract with the Championship side in 2016.
And the English left-back, who has made over 100 appearances for Reading, will be out of contract in the summer.
According to The Daily Telegraph, Bayern are now interested in bringing in the England under-21 international on a free transfer.
Richards, who has previously been linked with Everton, is free to speak with the defending German champions ahead of his contract expiring in June.
Bayern's plans for the Reading player remain unclear, especially as Alphonso Davies, Lucas Hernandez and David Alaba can all play at left-back.
Reading manager Veljko Paunovic addressed the uncertainty surrounding Richards and 19-year-old midfielder Michael Olise in December.
Paunovic claims that he advised the Reading board that both Olise and Richards should be part of the club's "long-term project."
The 43-year-old Serbian explained: "When I spoke with our senior board, I definitely encouraged for both to be part of our long-term project.
"I expect the club is working towards putting together the proper offer so we can keep them for the long term.
"We are all aware we want them to be with us for a long time. We're working towards that."
Richards has made 21 appearances across all competitions for Reading this season.
The Bayern target has also attracted interest from other Premier League clubs like Brighton, West Ham and Crystal Palace.
Featured Image Credit: PA
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