The Bavarians may have confirmed the addition of Dante on Thursday, but remain interested in the Germany international, however, S04 claim to be uninterested in a sale
The Bavarians expressed interest in the 24-year-old last summer, but were turned away as S04 refused to sell a second key player after Manuel Neuer made his move to Munich.
However, as Goal.com exclusively revealed in January, Schalke had agreed to listen to offers for Howedes after this summer's European Championship.
Publicly, Schalke's stance is clear that they will not sell their captain.
"Benedikt is a Schalke man and has no intention of leaving us - we are not thinking of selling him," sporting director Horst Heldt said.
However, Schalke's considerable debt and previous pledge to consider offers suggest that if the price is right, the Gelsenkirchen side will consider a Bayern approach.
Bayern have long been preparing for next season, with Basel winger Xherdan Shaqiri having confirmed his move to the Allianz Arena in February. On Thursday, the Bavarians announced a second addition in the form of Monchengladbach centre-back Dante.
Howedes, a native of Haltern, has been at Schalke since 2001. His contract is set to expire in 2014.