A fee has yet to be agreed between the clubs. Manchester City are expected to receive over £15 million for the 33-year-old.
However, the treble winners are understood to be reluctant to part ways with Walker, who has a year left on his contract. Manchester City have tried to convince him to ink a new deal, Honigstein adds.
Talks between Bayern Munich and the England international began in June.
Walker’s departure would leave Manchester City without a senior full-back, potentially forcing the Premier League champions to search the transfer market for a replacement.
Manchester City still have Joao Cancelo on their payroll but are reportedly eager to sell the Portuguese full-back. The team loaned Cancelo to Bayern Munich in January because he was apparently frustrated with his lack of playing time under Pep Guardiola last season.
Walker has won the Premier League five times since joining Manchester City from Tottenham Hotspur in 2017. He’s also won two FA Cups, four League Cups, and the Champions League.