Goretzka, 31, will become a free agent when his contract at Bayern Munich expires at the end of this month.
The Germany international midfielder, capped over 50 times by his country, had been linked with several European clubs in recent months as his Bayern deal wound down. He had the chance to leave in January, with Atletico Madrid reportedly interested in a quick-fire move, but he opted to stay and finish the season with Bayern.
Goretzka was subsequently linked strongly with AC Milan, with reports suggesting he had agreed personal terms with the Italian club on a three-year deal worth around €5m per season. However, that move collapsed after Milan failed to qualify for the Champions League and dismissed head coach Massimiliano Allegri along with several senior executives.
With the Milan move on ice, Goretzka's representatives are said to have reopened talks with other interested parties, including Juventus. According to The Athletic, Chicago Fire have now entered the race and have held discussions over a potential move to Major League Soccer.
The Fire are also working separately on a deal for Robert Lewandowski, 37, who is leaving Barcelona as his contract there comes to an end. Lewandowski has travelled to Chicago to hold talks with the club's hierarchy as he assesses his options for next season.
According to transfer journalist Fabrizio Romano, Lewandowski's representatives have accompanied him on the trip, with Chicago understood to be front-runners for his signature. The Polish striker, his country's all-time leading goalscorer, is also said to be considering offers from clubs in Saudi Arabia.
Goretzka and Lewandowski played together at Bayern Munich between 2018 and 2022, winning the Bundesliga and Champions League during that period. Should both moves go through, the pair would be reunited at Chicago Fire, who are looking to add experienced reinforcements to their squad.
Fire head coach Gregg Berhalter currently relies on Hugo Cuypers as his main striker, with the Belgian having scored 13 goals this season and earning a call-up to the MLS All-Star Game.
Adding Lewandowski to a squad that already features a prolific scorer in Cuypers could present a tactical question for Berhalter, given his preference for a single-striker system.
The Goretzka situation is described as further from completion than the Lewandowski talks, with the midfielder still weighing up interest from clubs across Europe. Goretzka is currently on World Cup duty with Germany under head coach Julian Nagelsmann, meaning any final decision on his future is likely to wait until after the tournament. For Chicago, completing either deal would represent a significant statement of intent, with the prospect of landing both representing what one report described as a "remarkable summer swoop".
Whether the Fire can compete with the financial muscle of European suitors for Goretzka remains to be seen, but their position in the race for Lewandowski appears considerably stronger at this stage.