The 17-year-old attacker is one of England's best players in his age group and has made four appearances for Antonio Conte's side this season.
Barcelona, Madrid and Juventus are the most high profile clubs to show interest, but a desire for first team football might give teams like Villarreal a chance against the European giants.
Chelsea will look to resist the sale of the academy graduate, but their expected absence from the Champions League next season along with a strong bid could give them an opportunity to make quick money to invest in their first team.
Hudson-Odoi won the Under 17 World Cup with England in 2017 and is keen to take his career to the next level.
English wonderkids Jadon Sancho, Ademola Lookman and Reece Oxford's exploits in the Bundesliga have inspired the next generation of youngsters to seek experience away from the super-rich Premier League.
Chelsea have won five successive FA Youth Cups, which matched the record of Manchester United's legendary Busby Babes, but that leaves five years of talent fighting for spots in the first team against the club's upcoming summer signings.
They also won a quadruple at Under-18 level after beating Manchester United in the national final and narrowly missed out on the UEFA Youth League, having lost in the final to Barcelona