Last summer, the Blues made the decision to strengthen their attacking ranks with Nicolas Jackson, Christopher Nkunku and Deivid Washington.
As it stands, only Jackson has proven to be a moderate success, with Nkunku spending much of his time injured and Washington regarded as one for the future.
With Armando Broja also seemingly being discarded and now on loan at Fulham, Chelsea will almost certainly be in the market for a new frontman at the end of the season.
However, how ambitious they get is largely dependent on their efforts to meet the Premier League's Profit and Sustainability regulations, Chelsea having recently posted losses of £90.1m for the 2022-23 campaign.
That effectively means that cutbacks and a substantial profit will need to be made in due course, particularly ahead of their next accounting date of June 30.
A return to the Champions League is out of the question, yet Mauricio Pochettino's side are still pushing for a spot in the Europa League or Europa Conference League, competitions that may still help their cause financially.
Nevertheless, according to TEAMtalk, Chelsea have both little desire and an inability to meet the current wage demands of top target Osimhen.
The report suggests that the Nigeria international feels that he is worth at least £200,000 per week, a figure that Chelsea are unlikely to commit to at the present time.
Each of Paris Saint-Germain and Arsenal are said to be growing in confidence that they hold a greater willingness to meet whatever Osimhen requests in his contract.
Despite the disappointment of likely parting ways with Kylian Mbappe, PSG will free up substantial space on their wage bill, while Arsenal allegedly plan to cash in on Eddie Nketiah.
From Chelsea's perspective, Osimhen has hinted in the past that moving to Stamford Bridge would be his ideal move, yet it appears increasingly unlikely that enough boxes will be ticked for the relevant parties to agree terms over a move.
Napoli president Aurelio De Laurentiis has already acknowledged that Osimhen will definitely leave the Serie A champions in the summer, and there is more chance of that happening if they miss out on Champions League qualification for 2023-24.
When Osimhen penned a new contract at the back end of 2023, it included a release clause said to be in the region of £112m.