The 25 year-old winger has attracted much interest from Premier League clubs including Manchester United and Liverpool.
The Reds have already been very active in the transfer window, spending around £60m so far and were set to break the £100m mark.
But according to reports emerging in Germany, Reus is interested in joining Bayern in a deal thought to be worth around £28m and the Dortmund man would be reunited with former team-mates Robert Lewandowski and Mario Gotze.
It is believed that Bayern manager Pep Guardiola is keen on signing Reus despite missing the World Cup in Brazil due to an ankle injury.
The potential move would be a massive blow for Liverpool, who are looking to strengthen their attack following the departure of key goalscorer Luis Suarez.
Meanwhile Frenchman Loic Remy is set to complete his switch to Anfield within the next 24 hours after QPR agree an £8.5m fee. Fabio Borini, who spent last season on-loan with Sunderland is expected to be sold for a reported £14m.
By Phil Wellbrook