The Yorkshire club have emerged as clear frontrunners for the 25-year-old largely because they are prepared to take him without any obligation to buy, a structure that suits Chelsea, who want to retain long-term control of his future while another club covers his wages this season, according to the BBC.
Negotiations are expected to continue in the days ahead.
Mudryk himself is understood to favour staying in the Premier League and has shown a preference for Elland Road, despite competing interest from Strasbourg — Chelsea's sister club under the BlueCo ownership group — and clubs in Italy. Both player and club have agreed that a season away from Stamford Bridge is the best route back to full match sharpness.
The winger spent 20 months out of the game after failing a drug test for the banned substance meldonium, a suspension that finally ended in July. Since then he has featured for Chelsea in pre-season under new head coach Xabi Alonso, coming off the bench in several friendlies as he works his way back to fitness.
Leeds United have already been busy this summer, bringing in four new faces: winger Harry Wilson from Fulham, centre-back Tarik Muharemovic from Sassuolo, goalkeeper James Trafford from Manchester City and defender Nico Elvedi from Borussia Monchengladbach. Their earlier interest in Chelsea forward Liam Delap has since cooled.
Brentford also looked at Mudryk but wanted an option to make any move permanent, a condition Chelsea turned down.
The Bees tried to sign the Ukraine international years before Chelsea beat them to his signature, paying Shakhtar Donetsk an initial £61m for him in January 2023, and they have not given up hope of doing business now.
Coventry City have also registered interest, and a switch to Strasbourg has not been ruled out, with Chelsea said to be weighing up sending other fringe players, such as midfielder Dario Essugo, to the French club as part of wider squad business.
Staying at Stamford Bridge remains the least likely outcome, though Chelsea have stopped short of closing that door completely.