The Bundesliga champions' new boss Pep Guardiola is a huge admirer of the £30m-rated Welshman, who on Friday was shortlisted for the PFA player of the Year award.
The former Barcelona manager is ready to snatch Bale from under the noses of old rivals Real Madrid, according to The Sun.
Guardiola followed Bale's progress for over a year when still at the Camp Nou, and he is now ready to make the 23-year-old his marquee signing when he takes over at Bayern in the summer.
Bale's exceptional performances this season have firmly established him as one of Europe's hottest properties.
Tottenham remain adamant their star player is not for sale and are preparing a lucrative contract offer.
However, if they finish outside the top four they will surely struggle to keep a player desperate for Champions League football.
On to another long-time target of Europe's biggest and richest clubs - Napoli striker Edinson Cavani.
The Daily Mail reports that Manchester City are close to winning the race to sign the Uruguayan thanks to a giant contract worth €300,000 (£256,000) a week.
That would make Cavani the highest-paid player in British football, eclipsing would-be team-mates Carlos Tevez and Yaya Toure.
Real Madrid and Paris Saint-Germain are also in the hunt for the 26-year-old, whom Napoli insist will not move for less than his £52m release clause.
For what it's worth, which may be very little, Cavani's mother Berta Gomez has said: "He told me he wants to elsewhere and to leave Napoli."
Manchester City also have their eye on Schalke defender Kyriakos Papadopoulos.
The 21-year-old Greek international has already been the target of bids from AC Milan and Zenit St Petersburg, but the Daily Star believes City are ready to land Papadopoulos by meeting his £16m release clause.
Chelsea are looking to add to their impressive array of attacking talent as they pursue a deal to sign German international Andreas Shurrle from Bayer Leverkusen.
The £20m-rated forward appears set for Stamford Bridge after Leverkusen's sporting director Rudi Voller held talks with Chelsea, the Daily Mail reports.
A season-long loan of Chelsea's Belgian midfielder Kevin De Bruyne, currently on loan at Werder Bremen, could be the key to sealing the deal.