Herrera only joined United over the summer from Athletic Bilbao but recent reports suggest he has failed to settle in Manchester.
Bayern are keen to strengthen their midfield in January, according to reports in Germany, with Christoph Kramer, Sami Khedira and Lars Bender all also under consideration.
But Pep Guardiola, who wants Herrera to play alongside compatriot Xabi Alonso at Bayern, is hopeful sending Shaqiri to Old Trafford could pave the way for a deal to go ahead.
GETTY
Ander Herrera could be used as bait for Xherdan Shaqiri
Bayern Munich want another midfielder in January
Liverpool are also known to be keen on the Swiss winger, who has grown tired of his lack of opportunities at the Allianz Arena.
It has been suggested that United would demand £21m to let Herrera leave, but with Shaqiri valued at £15m, only £6m could change hands.
It now remains to be seen whether United are really ready to cut ties with Herrera after just six months in England, and whether Bayern will prefer the 25-year-old to the other players on their wish-list.
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