The league says the consortium has passed its owner's and directors' test.
The Premier League club was put up for sale before owner Roman Abramovich was sanctioned over his links to Russian president Vladimir Putin.
The purchase remains subject to the Government issuing the required sale licence.
The final stages of the transaction will then need to be completed.
The government does not want Abramovich to make any proceeds from the sale but sources are optimistic about a deal being finalised on Tuesday night.
"We now believe everyone will be ready to issue the necessary licences" said one insider to BBC Sport.
"The last remaining hurdle boils down to a number of final technical details that are being discussed with the club."
Several parties expressed an interest but Chelsea agreed to sell to the Boehly-led consortium earlier in May.
The consortium is led by Boehly but Clearlake Capital, a Californian private equity firm, would own a majority of the shares in Chelsea. Other investors include US billionaire Mark Walter, also a co-owner of the LA Dodgers, and Swiss billionaire Hansjoerg Wyss.
Chelsea have been allowed to continue operating under a special government licence which expires on 31 May.
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