The Ukraine international, 25, has not featured competitively since November 2024, when he was suspended for four years after returning an adverse finding for the banned substance meldonium.
An agreement was later reached to resolve the doping case, clearing Mudryk to resume his career, and he has since made substitute appearances in pre-season friendlies against Juventus, AC Milan and Johor Darul Ta'zim during Chelsea's tour of Asia.
In meetings held at the end of that tour, Mudryk agreed to leave on loan before the transfer deadline on 1 September. A move to Strasbourg, who share the same BlueCo ownership as Chelsea, has been proposed, but the winger would prefer to stay in England and join another top-flight club instead.
Several other sides have also emerged as potential destinations, including a number of leading clubs in Italy.
Mudryk remains under contract at Stamford Bridge until 2031, having joined from Shakhtar Donetsk for an initial £61 million in January 2023. He made 73 appearances for Chelsea before his ban, scoring nine goals, and had shown flashes of the form that persuaded the club to make him one of their most expensive signings, contributing three goals and three assists in six Conference League appearances during the 2024-25 campaign before his case began.
Any loan would give Mudryk the platform to rebuild his sharpness away from the pressure of competing for a place in Xabi Alonso's squad, which already features Pedro Neto, Jamie Gittens and Estêvão among the attacking options.
Mudryk himself has spoken of relief at finally being free to play again, describing the case as the most difficult period of his career after changes to anti-doping testing standards played a part in the resolution.
With the transfer window closing in three weeks, Chelsea are working to find a solution that both protects the player's long-term value and gets him back playing regular first-team football as soon as possible.