Sanchez's future at Arsenal beyond this summer is uncertain after a campaign that saw him score 30 goals and fire the club to the FA Cup.
The Chile international's current contract expires next year and, as of yet, they are yet to convince him to sign an extension.
Premier League duo Chelsea and Manchester City have both been backed to make a move for him, while Manchester United have also been linked with him.
Across Europe, however, Paris Saint-Germain and Juventus are also watching his situation with great interest.
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Bayern Munich are confident of signing Arsenal star Alexis Sanchez
However, The Mirror claim Bayern feel they will win the race for Sanchez – and reunite him with compatriot Arturo Vidal in the process.
Vidal admitted earlier this week he was doing everything he could to ensure Sanchez moves to the Allianz Arena, and his efforts appear to be working wonders.
Bayern have reportedly held talks with the player's representatives and, after encouraging talks, are ready to make a bid to lure him to Bavaria.
Arturo Vidal is encouraging Alexis Sanchez to swap Arsenal for Bayern Munich
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Arsenal's reluctance to sell Sanchez to a domestic rival seems to have swung the pendulum Bayern's way, with Carlo Ancelotti desperate to sign him as a long-term replacement for Franck Ribery.
The report adds that, though the winger has told Arsenal he intends to stay, manager Arsene Wenger is wary of him running his contract down and leaving on a free transfer next summer.
Sanchez has been a big hit at Arsenal since signing from Barcelona in 2014, scoring 72 goals from 145 appearances.
But, given the club's failure to win the Premier League title, the 28-year-old is looking increasingly likely to be playing his football away from the Emirates next season.