Earlier this year, the Blues were keen to sign the 18-year-old on a long-term contract, only for government-imposed sanctions to be placed on the club as a result of Roman Abramovich's links to Russia president Vladimir Putin.
However, it was confirmed on Saturday morning that the Premier League club are close to be taken over by a consortium led by Todd Boehly, a development which means that Chelsea will be able to resume activity in the transfer market.
According to football.london, Chelsea remain impressed with the teenager, who has made 13 starts in the MLS during the current campaign.
Although Chicago Fire sit at the bottom of the Eastern Conference, Slonina has conceded just 17 goals, a return which has not gone unnoticed by other clubs.
The report claims that Bayern Munich and Wolverhampton Wanderers are also monitoring the situation but are yet to meet Fire's valuation.