Reports in Germany emerged on Thursday claiming Bayern Munich had reignited their interest in the 18-year-old winger.
The Bavarian giants had four bids rejected for the England international, who is out of contract in 2020.
However, the Telegraph says Hudson-Odoi is nearing an extension with the west London outfit.
The imminent arrival of Frank Lampard as manager has played a part in Hudson-Odoi's decision.
He will be sidelined until September with an Achilles injury suffered last season.