Abramovich wants to sell the Stamford Bridge club after 19 years, following his homeland Russia’s invasion of Ukraine.
Little-known Turkish businessman Bayrak is one of those interested in buying the Blues and has already opened negotiations.
He told Turkish broadcaster Oda TV: “We have reached a certain stage. Our law and finance department will start talks with theirs in London on Thursday.
“That’s the way it is at this point. On Thursday, we will notify the Public Disclosure Platform (KAP).
“People are talking about it, we made some progress in the talks, and the world believes we have a 90% chance of completing the deal. Abramovich thinks the same.”
It is understood that Abramovich’s asking price is £3billion, but Bayrak claims they will buy for less.
He added: “We didn’t give that price (£2.5bn) to the British press. Our offer is under that, I’ll at least say that.”