Boehly has had a falling out with his fellow Blues owner, Behdad Eghbali, leading to speculation that one of them may be looking to buy out the other at the club.
The Sun says with Eghbali's Clearlake Capital the majority owners, they can block Boehly from selling his shares.
As part of their agreement, Clearlake can block any sale of their partner's shares. Clearlake hold 61.5 per cent of Chelsea's shares.
Boehly and fellow investors Hansjorg Wyss and Mark Walter hold the remaining shareholding.
Given the tension, it's been suggested Clearlake will offer to buy their partners - including Boehly - out completely.