The Magpies are keen to add further depth to their attacking options and are believed to have placed the three-times capped England player on their list of possible targets.
Hudson-Odoi actually made his Chelsea debut against United when he replaced Pedro in a 3-0 FA Cup win over the Magpies in January 2018.
He went on to play under successive Blues coaches with Antonio Conte, Maurizio Sarri, Frank Lampard and current manager Thomas Tuchel all handing opportunities to the Wandsworth-born star.
However, the winger is said to have become frustrated over a lack of consistent game-time and Sky Sports have reported he has been given permission to negotiate a loan move away from Stamford Bridge.
Newcastle, Borussia Dortmund, Leicester City and Southampton have all been named as potential destinations and a further update was provided by journalist Fabrizio Romano over the weekend.
He tweeted: “Callum Hudson-Odoi could now leave Chelsea for regular game time.
“Southampton have already asked for CHO on loan, now pushing. He was also discussed with Leicester days ago – it’s up to the player.
“Hudson-Odoi will make a decision on his future in the coming days.”
Magpies manager Eddie Howe discussed his desire to add further new faces to his squad following Saturday’s season-opening 2-0 home win against Nottingham Forest.
Summer signings Nick Pope and Sven Botman both made their competitive debuts against Steve Cooper’s side and Matt Targett made his first appearance since joining the Magpies on a permanent deal from Aston Villa.
The United manager said: “I’m not aware that anything has changed on that front, and I don’t anticipate that to be the case because everyone has been concentrating on the games, and rightly so.
“I don’t think today changes anything from my view. My squad is an excellent squad of players.
“I love the individuals we have, but I’d like to add some more quality to that if possible.”