The Blues say they have ended talks with Leeds over the 25-year-old Ukraine international after negotiations continued throughout the weekend.
Other solutions include a move to sister club Strasbourg or to another Premier League side. The newly promoted Sky Blues, along with Italian sides Napoli, Atalanta and Roma have shown interest.
Chelsea are keen to guarantee playing time for the forward, who joined from Shakhtar Donetsk for an initial £61m in 2023, by including financial penalties if he is not involved.
However, a move to Leeds was believed to be Mudryk's favoured option, with also having had an approach turned down over attempts to include an option to buy.
Mudryk is keen to get his career back on track after testing positive for the banned substance meldonium and serving a 20-month ban.
He returned to action at the end of July and featured in Chelsea's pre-season tour of Asia.
