Potential interested parties have until March 15 to submit offers to the New York merchant bank Raine Group, appointed to handle the sale of the club.
Sources have told ESPN that a consortium including Los Angeles Dodgers and LA Lakers part-owner Todd Boehly alongside Swiss billionaire Hansjorg Wyss have already tabled a bid in an effort to push ahead in the race.
Although the exact amount of their offer has not been made public, sources have told ESPN it does not meet Abramovich's asking price for the reigning world and European champions.
Boehly had a £2.2 billion ($2.89 bn) offer rejected in 2019 and is thought to believe the club has not significantly appreciated in value since then, given the COVID-19 pandemic and Russia's invasion of Ukraine, which has put Abramovich under pressure to reconsider his investments in the west.
Turkish businessman Muhsin Bayrak has claimed he submitted an offer "under £2.5bn ($3.29 bn)" and remains in talks while there is also rumoured interest from the Middle East but as things stand, more credible bidders to Boehly's group are expected to originate from elsewhere.
Sources told ESPN last week that RedBird Capital Partners, the Manhattan-based private equity company founded by Gerry Cardinale and advised by Oakland Athletics executive vice president Billy Beane, are one of a number of US-based groups assessing the feasibility of a bid.
There is speculation US businessmen Josh Harris, part-owner of the Philadelphia 76ers, and New York Jets owner Woody Johnson are separately considering entering the running. The Ricketts family, who own the Chicago Cubs, have been named as another interested party.
British property developer Nick Candy is also weighing up an offer at around £2.5bn ($3.29 bn) with his spokesperson confirming he is "actively exploring a number of options."
However, no party has expressed a willingness to pay Abramovich's asking price for several reasons, not least the difficulty of redeveloping Stamford Bridge -- a complex project in one of the most expensive parts of London anticipated to cost in the region of £1.5bn ($1.97 bn).
The March 15 deadline is also significant as it is the day the UK government will be able to impose tougher sanctions on high net-worth individuals with any links to Russia or President Vladimir Putin.
Emergency legislation known as the Economic Crime Bill aims to crack down on foreign criminals using UK property or assets to launder money. Abramovich has always strenuously denied any ties to the Putin regime or any business impropriety but he has faced calls from a number of MPs including Labour leader Sir Keir Starmer to face sanction.
It is unclear at this stage whether Abramovich would be targeted by this new legislation but the possibility adds an extra urgency to the pace of negotiations over Chelsea's sale, which sources claim some interested parties believe could push him into accepting a figure below his £3bn ($3.94 bn) valuation.