Todd Boehly and Clearlake Capital have, so far, endured a summer largely focused on facilitating as many sales as possible in order to meet FFP regulations.
As it stands, 13 players from last season's squad are no longer present, 10 departing on permanent deals, David Datro Fofana going out on loan to Union Berlin and each of Denis Zakaria and Joao Felix returning to Juventus and Atletico Madrid respectively.
Further departures will occur in due course, yet Mauricio Pochettino has acknowledged that he is keen to add to the signings of Christopher Nkunku and Nicolas Jackson as soon as possible.
A new centre-back and central midfielder are at the top of Pochettino's priority list, Chelsea one defender down due to the serious knee injury sustained by Wesley Fofana and the club known to be interested in acquiring Brighton & Hove Albion's Moises Caicedo.
Nevertheless, Chelsea are also in the market for a new forward, whether that be a recognised number nine or a player who can feature in a number of roles in the final third.
According to RMC Sport journalist Fabrice Hawkins, Chelsea are contemplating whether it is worth putting forward a proposal for Mbappe.
The France international said earlier this summer that it was his intention to see out the remaining 12 months of his PSG contract before leaving on a free transfer, a stance which has swiftly led to his club putting him up for sale.
Mbappe has been left out of the squad for the pre-season tour of Japan and South Korea and allegedly put up for sale by president Nasser Al-Khelaifi.
Whether a sale is realistic remains to be seen, with long-term suitors Real Madrid not in a position to meet PSG's demands this summer and minimal clubs in Europe having the financial firepower to sign the 24-year-old.
However, Saudi Pro League club Al-Hilal may allegedly emerge as the frontrunners, the report stating that PSG would accept a bid of €200m (£173.11m).
While Chelsea are yet to make a bid for Mbappe, they are reportedly holding internal discussions to consider whether it is plausible to meet PSG's valuation.
Although the Premier League outfit would not be able to offer European football for 2023-24, Chelsea are now managed by Mbappe's former PSG boss Pochettino and could be in a position to meet the player's wage demands once further sales have materialised.