The Bavarian giants are keen to add new quality to their squad, and remain intent on signing the Germany international having prepared a player-plus-cash offer
The 24-year-old Howedes has long been linked with Bayern, with the club having had an offer rejected last season due to Schalke's unwillingness to part ways with a second key figure after selling Manuel Neuer. However, as Goal.com revealed in January, the Gelsenkirchen side promised to listen to offers in the summer of 2012.
Publicly, Schalke have vowed not to sell their captain, with sporting director Horst Heldt having claimed in April that his side are not interested in selling the Germany international, nor does the player wish for a transfer.
"Benedikt is a Schalke man and has no intention of leaving us - we are not thinking of selling him," he told der Westen.
Schalke have considerable debt, however, and as Goal.com revealed in January, are prepared to listen to bids in the region of €15m.
Bayern's reported offer would see Rafinha reunited with his former club, which he left for Genoa in 2010. However, with the Brazilian having been relegated to a role as a bench-warmer over the course of the recent season, it is uncertain that Schalke will value him as highly as Bayern.
Howedes, a native of Haltern, has been at Schalke since 2001. His contract is set to expire in 2014.