Mane has also reportedly attracted interest from Manchester United and Chelsea.
Mane seems to be in high demand at present, with Manchester United registering a bid for him last summer, according to Sky Sports, while the Daily Mirror has recently reported that Chelsea are admiring the Senegal star.
The Telegraph's report states that Southampton don't feel under any pressure to sell the player, who is under contract at St Mary's until 2018, but there is a lot of focus on United's interest in the 23-year-old.
It's perhaps of little surprise that Mane is attracting interest from some of Europe's top clubs given the impact he has had since arriving at St Mary's, which saw him score the fastest Premier League hat-trick towards the end of last season, part of a 10-goal haul for the Saints, while he has already found the net on seven occasions in all competitions so far this season.
Bayern are looking at Mane after injuries that have been sustained by Arjen Robben and Franck Ribery this season. One would question whether Mane would be wise moving to the Bundesliga champions, where there is such a fierce competition for places, as there is certainly no guarantee of regular game time, given the star names that are likely to be ahead of him, in the short-term at least.
Given that Southampton stood firm in the summer over Mane, it would take a huge offer to tempt them to part with one of their more pivotal players.