The England Under-19 international has this month been the subject of four bids from German giants Bayern Munich.
Chelsea have rejected all of Bayern’s advances for Hudson-Odoi, including a £35million offers.
Hudson-Odoi handed in a transfer request last week in order to force through a move to Bavaria but had it rejected.
Chelsea have remained steadfast in their unwillingness to sell the 18-year-old, who reportedly still harbours hope of leaving Stamford Bridge.
According to Goal, Hudson-Odoi is ‘hopeful’ the Blues will soften their stance and will allow him to pursue a move to Germany in the summer.
The news of Hudson-Odoi’s intention to leave Chelsea at the end of the season came shortly after Bayern Munich boss Robert Kovac ruled out a deadline-day swoop for the midfielder.
“We will no longer be active in the transfer market,” he said.
“The teams do not want to let their players leave. We have a good and big squad.
“I have to leave one or two at home again this weekend (when they face Bayer Leverkusen).”
Bayern are expected to renew their interest in Hudson-Odoi in the summer, and former Blues defender William Gallas has urged his old side to do everything in their power to keep him in west London.
In an interview with Leo Vegas, the Frenchman said: “The question is, why would Chelsea be willing to sell Callum Hudson-Odoi?
“The player has a lot of quality and, if he still works hard at training, if he keeps playing games in the Premier League or in cup competitions, he will keep improving.
“Maybe one day he can even replace Eden Hazard.
“But you can’t sell one young player who has a lot of quality, you have to keep him.”
Hudson-Odoi and his Chelsea team-mates will next be in action on Saturday afternoon, welcoming Huddersfield to Stamford Bridge.
The Blues will go into the match on the back of a 4-0 drubbing at the hands of Bournemouth, a defeat which saw them relinquish fourth place to Arsenal.