Russian Abramovich put the club up for sale in early March following his country’s invasion of Ukraine.
The British government demanded assurances that Abramovich, who was sanctioned following the invasion – which Moscow calls a special operation – will not benefit from the sale.
The London club earlier this month announced the 4.25 billion pound ($5.2 billion) deal with Boehly’s consortium, backed by Clearlake Capital, for the reigning European champions, subject to receiving the required approvals.
The UK government’s approval of the sale was being finalised on Monday night, the source said, though the deal also faces the need for EU approval, as Abramovich holds a Portuguese passport.
The Financial Times and the BBC were the first to report the pending approval of the sale by the government.
(Reporting by Alistair Smout; Editing by Ken Ferris)