The former No. 23 was given a clear path to find a new home last summer after three years on Merseyside, with Lyon his chosen destination after 63 appearances for the Reds.
He has made 16 appearances for Peter Bosz’s side, 13 of those from the start with a record of two goals and three assists, but he was left out for Saturday’s meeting with Monaco.
And Lyon confirmed it was due to the club granting Shaqiri permission “to start discussions with an MLS club as part of a future transfer.”
The Major League Soccer side in question is Chicago Fire, with the MLS website claiming the deal is “at an advanced stage”, with a fee in the region of £5.49 million being mooted.
Notably, Chicago Fire’s sporting director Georg Heitz worked for Basel at the same time Shaqiri broke through as a teenager.
He would be the latest to swap Europe for the United States, with Lorenzo Insigne to join Toronto FC and ex-Bayern Munich man Douglas Costa landing at LA Galaxy.
Occupying one of the three designated player spots on Chicago’s list means he will be considered outside of MLS’ stringent salary cap, Gaston Gimenez is also categorised as a designated player.