The Blues were one of several clubs who were heavily linked with the Nigeria international before he eventually departed Napoli for Turkey in a season-long loan switch.
Although Osimhen was not prioritising a move to Galatasaray, he has fitted in seamlessly to help the defending champions sit clear at the top of the Super Lig standings.
Furthermore, the 25-year-old has chipped in with four goals and two assists from his five appearances in the division, Galatasaray already scoring 29 times in 10 matches.
Nevertheless, as part of the deal that has taken him to Rams Park, it is known that certain clauses and options become relevant at the midway point of the campaign.
Chelsea suffer Osimhen blow?
Osimhen is said to have the option of cutting short his time with Galatasaray should a higher-profile team make a suitable offer to parent club Napoli.
A release clause in the region of £63m is said to be present in their agreement, one that Chelsea may plausibly look at activating on the basis that it is considerably lower to the fee that was required in the summer.
However, as per Turkish outlet Sozcu, Galatasaray are ready to make their own bid to sign Osimhen on a permanent basis in January.
The report alleges that a sponsor may help the current league leaders fund a £42m approach for the frontman in a bid to edge out rivals for his signature.
Notably, Galatasaray have never paid more than £15m on a single player, emphasising their desire to retain Osimhen's services in the long term.
Would Chelsea react?
While Chelsea were seemingly eager to get a deal over the line for Osimhen in the summer, it is unclear whether things have changed at Stamford Bridge.
Nicolas Jackson has since contributed six goals and three assists in the Premier League, as well as signed a new nine-year contract.
Christopher Nkunku is already at the club as backup with eight goals to his name in all competitions, while youngster Marc Guiu is viewed as third choice and an option for Conference League games.
Chelsea also possess the third-best attacking record in the Premier League, scoring 20 times during their opening 10 fixtures.