The 18-year-old shone during pre-season and took advantage of the late return of the club's World Cup stars to start against Manchester City in the Community Shield in the season's traditional curtain-raiser.
However, he has failed to force his way into Maurizio Sarri's thinking since, making just two substitute appearances in the Europa League.
Nevertheless, he remains highly thought of at Stamford Bridge and it is hoped that a loan to a Premier League side in January could be the perfect next step in his development.
According to the aforementioned source, the 'Blues' see him as ready for senior football and would prefer to loan him to a side struggling at the wrong end of the table, with Burnley and Southampton both understood to be among the potential destinations for the England U19 international.
Both sides are believed to be keen on adding wide options to their ranks come the turn of the year and with young English talent top of their wishlists, Hudson-Odoi's availability is believed to have pricked more than a few ears at St Mary's and Turf Moor.