The Daily Mail says the 18-year-old England star has Bayern Munich, Paris St Germain and Juventus keen to sign him this summer or in January, when he will have just six months left on his deal and can then commit to a European team with only minimal compensation due to Chelsea.
There is a possibility the forward, currently injured with a ruptured Achilles, will consider signing a deal if the club show they are planning to build the team around him in the future.
With Hazard leaving when a fee can be resolved with Real Madrid, there is an opportunity to pass the creative leadership of the team on to Hudson-Odoi.
That is the pitch Bayern made to him. They made it clear he would wear the No 10 shirt of Arjen Robben, who is leaving the club, when they made their £35m bid in January.