Inter Miami have also been linked, but they cannot talk to Lewandowski while he remains on that list, with Fire in pole position should he decide to continue his career in America.
Lionel Messi’s Inter side have one of their designated player spots open after Jordi Alba’s retirement following their first-ever MLS Cup victory against Vancouver this month.
Fire – who also tried to sign Neymar and Kevin de Bruyne earlier this year – have made Lewandowski a priority for at least six months – a strategic move as Chicago has the USA’s largest Polish community.
The former Bayern Munich and Borussia Dortmund forward’s wife, Anna, visited Chicago last month while in the States.
Lewandowski has 109 goals in 164 games for Barcelona, twice winning La Liga, since joining in 2022 on a four-year deal.
He has scored eight goals in 17 appearances this term, with his side four points clear at the top of La Liga.
Additional reporting from Nizaar Kinsella.