Shaqiri is set to play against Bayern on February 22nd in the Champions League, Round of 16, first-round clash in Basel with the return match in Munich on March 13th.
The 20-year-old arrived in Munich on Tuesday with his agent and his brother and was photographed at Bayern's training centre.
The Swiss star underwent a medical while his agent spoke with Bayern's director of sport Christian Nerlinger, according to German daily Bild.
After Bayern missed out on signing Borussia Mönchengladbach's Marco Reus, who will join Dortmund next season, Munich are reported to be set to offer Shaqiri a four-year deal.
"The transfer makes sense," Swiss coach and former Bayern boss Ottmar Hitzfeld told Bild.
"I told (Bayern chairman) Uli Hoeness a year ago that Xherdan is an outstanding player, someone who can easily adapt and evolve to play at the highest level."