Gikiewciz, 27, is a free agent after leaving Bulgarian club Levski Sofia last month, following a brief four-month spell which saw him score three goals in nine total appearances.
The 6ft 2in front man has struggled to settle since leaving Poland’s Slask Wroclaw for Cypriot out Omonia in 2013, having had further stints with Kazakhstan’s FC Tobol and AEL Limassol over the past 12 months, and is now being linked with a move across the Atlantic.
The Chicago Fire, Orlando City SC and Philadelphia Union have all been named as prime suitors but Celtic and Hull are also reported to be in discussions with his agent about a potential deal.
However, speaking to the Chicago-based Herald, Gikiewicz himself revealed that he would be keen on a move to the Fire, who have had a number of his compatriots on their books in the past, including former internationals Piotr Nowak and Tomasz Frankowski.
"Many clubs are showing interest lately, including Chicago," he said. "I think any Polish player would be honoured to play there. Currently, I am looking for a stable move; a club that is committed to me and my future."
Agent Valentin Macovei added: “We are currently assessing options, but I think Chicago would be very good for both the club and the player. Lukasz will not only add goals and assists to the club, but also a few thousand more Polish fans to fill up Toyota Park.
“When the club was founded they had a few Polish players, why shouldn't they continue by following their tradition?"
A strong forward who is dangerous in the air, Gikiewciz featured in the Europa League last term for AEL, when he started both legs of his side’s 5-1 aggregate defeat to Tottenham Hotspur in the competition’s playoff-round.
Having never managed more than nine goals in a season, it remains to be seen whether he could offer either Celtic or Hull much but, given the lack of transfer fee, there would not be much risk attached to his potential signing.