Earlier this month, it was widely claimed that Real Madrid were highly likely to win the race for the 18-year-old, who is already impressing in the MLS.
His representative Jaime Garcia even went as far as saying that the Bernabeu was his preferred destination, telling MLSSoccer.com: "It should be an honor for Chicago, and MLS, to have Real Madrid take notice in one of their players. We are hoping Chicago can find an agreement with Real Madrid to realize Gabriel's dream of playing for this club.
"With respect to other clubs and other offers - we've received many and we are gracious to those clubs - but you cannot say no to Real Madrid."
However, that no longer appears to be the case, transfer expert Fabrizio Romano claiming that Chelsea are now expected to get a transfer for the teenager over the line.
Real Madrid have allegedly failed to progress talks with Chicago Fire, seemingly gifting Chelsea a window of opportunity to step in and initiate negotiations.
Unlike Los Blancos, the Premier League giants are allegedly prepared to meet Slonina's asking price, said to be €10m (£8.53m).
Should Chelsea sign the prospect, it is currently unclear whether Slonina will spend the rest of the campaign with Chicago Fire or immediately make the switch to Stamford Bridge.
Chicago Fire and the youngster's representatives will likely point to his development being best spent in the United States for the time being, a result of 14 starts having been made this campaign.
However, much could depend on how Chelsea resolve the future of Kepa Arrizabalaga over the coming weeks, the Spaniard currently being tipped to move elsewhere.
Chelsea have other goalkeepers on the books, with Marcus Bettinelli acting as number three this season and Nathan Baxter having gained regular action on loan at Hull City.
Nevertheless, head coach Thomas Tuchel may insist on a more high-profile name to act as deputy to Edouard Mendy given Chelsea's commitments in several competitions.