The two sides are being linked with a move for the 22 year old who recently admitted he may leave the German giants in search of regular first team football.
According to The Daily Star, it appears that the Reds have the inside track after launching an €18 million bid for the former FC Basel player.
Shaqiri is a thought to be available as he is behind both Franck Ribery and Arjen Robben on the depth chart for the Bavarians.
Shaqiri made a total of 27 appearances in all competitions scoring seven goals and adding four assists.
He has made 33 appearances for the Swiss national team including the team’s 2014 World Cup opener against Ecuador.