The 25-year-old was recently cleared to return to football with immediate effect after his four-year doping ban was overturned.
Mudryk hasn’t played a competitive game for Chelsea since November 2024 but has been given chances by new manager Xabi Alonso during pre-season.
It’s understood that both the player and the club are keen on securing a loan move for 2026-27 as he seeks to get back to full fitness.
Per BBC Sport, Leeds have made an offer to take the winger for the season, but Chelsea have turned it down.
It’s understood the opening offer fell well short of Chelsea's expectations, but negotiations are ongoing with Mudryk wanting the move.
Frank Lampard’s Coventry City have also expressed an interest, while a move to Strasbourg remains under consideration.