The Bayern Munich target is growing increasingly frustrated with the lack of first-team football, despite assurances from Maurizio Sarri that he is ready for big games, and could end up hitting Chelsea's pocket.
Bayern have made no secret of their interest in the 18-year-old and have floated a figure of £35million in order to secure his services.
But Chelsea are not willing to sell the winger, whose contract expires in the summer of 2020.
According to the Mail, Hudson-Odoi is desperate to make the move and will refuse any offer from Chelsea in a bid to force their hand.
He doesn't plan to make life at Stamford Bridge uncomfortable by refusing to play, or going on strike, but he wants regular game-time and thinks his career will take off in Germany.
Sarri, however, has different ideas about what is in the winger's best interest.
The Blues chief stated that jumping ship would not be a good career move for the youngster and offered Hudson-Odoi a future within his squad.
However, Bundesliga veteran Arjen Robben has urged the 18-year-old to quit Chelsea and join Bayern.
If Chelsea refuse to budge on their current stance then they could miss out on the opportunity to cash in on the youngster who could hold out until next January when he would be free to negotiate with European clubs, such as Bayern.
The German champions have made a fourth offer of £35 million to sign the winger which meets Chelsea's valuation, but the Blues are not budging.
If they do not accept the deal that is currently on the table, Chelsea could stand to lose out on more than £34 million and be compensated with just £500,000 for the highly-rated youngster.
Chelsea would only be entitled to Fifa's training compensation fee, which is believed to be just half a million pounds, if Hudson-Odoi sticks at Stamford Bridge until next January and negotiates, freely, with overseas clubs.
When a player moves abroad, under the age of 24, Fifa's guidelines suggest that the club purchasing the player stumps up a fee for every year he has trained with the club, since the age of 12- this is thought to only be £500,000 for Hudson-Odoi.
Sarri has been less than impressed with Bayern's approach.
Speaking about the German's interest, the Blues chief said: "I think it is not professional.
"They are talking about a player under contract with Chelsea, so they didn't respect our club I think.
"I am very happy with the player, he is improving a lot.
"He needs to move in some moments without the ball. I would like to have him in the future."
Hudson-Odoi has not featured much for Chelsea this season, having only managed 50 minutes in the Premier League.
He was gifted a start in their FA Cup victory over Nottingham Forest and scored once during his two appearances in the Europa League.
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