Glasner has announced he will be leaving Palace when his contract expires at the end of the season.
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Current coach Kasper Hjulmand's future at Bayer uncertain, as they sit in sixth place on the Bundesliga table, four points outside the top four.
BILD says should they choose to shift out the Dane, Bayer see Glasner their top choice to be brought in.
However, the Austrian will need some persuading as he favours remaining in the Premier League rather than returning to German football.
Glasner enjoyed previous success at Eintracht Frankfurt - which he led to the Europa League title.