Hudson-Odoi has refused to sign a contract extension with the Blues, meaning he will become a free-agent in 2020.
However, Chelsea are willing to forego millions of pounds in order to keep the 19-year-old academy graduate for one more season.
The west London club could be unable to sign any players this summer, should they fail to overturn FIFA's transfer ban.
The London Evening Standardclaims Hudson-Odoi has rejected a contract offer worth £85,000-a-week, and will continue to hold out for £100,000-a-week.
A number of clubs, including Bayern Munich, are interested in the talented winger.