The Belgian looks increasingly likely to leave Stamford Bridge for Real Madrid at the end of the season.
Faced with losing their best player and the impending transfer ban, securing the future of a bright young talent like Hudson-Odoi has become a priority.
Chelsea rejected a series of offers for the England teenager from Bayern Munich and hope to entice him into staying when talks begin over a new deal.
Taking over Hazard's No 10 shirt, which he has held since joining in 2012, is key to this, claim Goal.
The 18-year-old's desire to leave has softened since January, the report claims.
Hudson-Odoi started four Premier League games in a row before suffering an Achilles tendon rupture against Burnley last month.
He is keen to resolve his future now as he gets set to spend a spell on the sidelines after undergoing an operation.
It is unlikely his future will be discussed until after the Europa League against Arsenal on May 29.
By Ayodele Emaye