Last week, he travelled with the team to Everton hoping to get some minutes but was left out of the squad entirely as Chelsea picked up their first three points of the season at Goodison.
Newcastle have the finances to support his heavy wages, as he is on good money at Chelsea, but there are remote concerns over his fitness, having been injured for a while last season.
Southampton are also interested but they will have to convince the youngster to take a pay cut or get Chelsea to pay a chunk of his wages if the deal is to make sense.
Hudson-Odoi, as well as other Chelsea players who did not take part in the game against Tottenham, was set to play in the developmental game this evening.
But he will not be taking part as discussions continue over his future.
Chelsea have brought in Raheem Sterling, Kalidou Koulibaly, and Marc Cucurella but there are a number of players in and around the team who are looking to move elsewhere for game time.
Thomas Tuchel is aware there are some unhappy players in his squad but says he would urge them all to fight for their spot.
He told the press: “In general, nobody is for sale and everybody is for sale.
“It depends on what the player wants, how bad the player wants it, what we think, who is ready to pay a certain amount of money.
“Then, maybe, everybody is for sale.”
He added: “But for Callum, it’s the same.
“He competes. He had a long-term injury and long-term problems to overcome from which he suffered.
“He has still a way to go to live up to his potential, because the potential is huge.”