The Blues boss is out of contract at the end of the season, but has put talks over a new deal on hold.
Die Knappen parted company with Dutch coach Stevens in December and appointed Jens Keller on a short-term basis.
He has managed to resurrect Schalke's season, putting them back on course for qualification to the Champions League.
However, the Daily Mail reports that the Bundesliga outfit are keen on landing a more experienced manager to the helm, and believe that the Scot is willing to listen to their offer.
Moyes, who has previously expressed a desire to coach in Germany, is the third-longest serving manager in the Premier League having taken charge at Goodison Park in 2002.