The Bundesliga giants are keen to sell Alcantara this summer.
The 29-year-old’s current deal expires next year and Bayern do not want him to walk away as a free agent.
Alcantara had been heavily linked with a move to Liverpool, with Jurgen Klopp a big admirer of the Spaniard.
The Reds may now be forced to step up their pursuit of the player, after Arsenal made enquiries.
It is however understand that both clubs are reluctant to meet Bayern’s £23million asking price.