The 29-year-old has not turned out for the Red Devils since the middle of February due to injury; he was able to recover to represent England in the latter stages of Euro 2024, but a calf problem has prevented him from making a single first-team appearance during the 2024-25 campaign.
Ahead of his departure at the end of last month, ex-Man United head coach Erik ten Hag said that Shaw had suffered a setback in his recovery process.
However, the 29-year-old was able to return to training alongside his teammates on Friday morning, and he could be available for selection soon after the international break.
Providing that his recovery continues to go as planned, there is a slight chance that Shaw may be in the squad for Ruben Amorim's first game in charge of Man United, which comes against Ipswich Town on November 24.
Shaw back in first-team training for Man United
Man United have continued to struggle at left-back this season, with Diogo Dalot, Noussair Mazraoui and Lisandro Martinez all looking unconvincing in that area of the field.
Shaw could be perfect for the left-sided wing-back role under Amorim, though, should the Portuguese decide to implement the 3-4-3 system that he has used successfully at Sporting Lisbon.
Man United's injury problems are now easing, with Tyrell Malacia and Leny Yoro also back in training, while Mason Mount and Christian Eriksen were involved off the bench against PAOK on Thursday night.
Interim head coach Ruud van Nistelrooy has also provided a positive update on Kobbie Mainoo ahead of Sunday's Premier League clash with Leicester City.
Mainoo has been out since early October with a muscular problem, but Van Nistelrooy has revealed that the England international is "making the right steps", as he looks to return soon after the international break.
Van Nistelrooy provides positive Mainoo update
Man United are also "working" to make sure Amad Diallo, who scored a brace against PAOK in the Europa League on Thursday, is available for Sunday, as he suffered a knock in the latter stages of the team's last match.
"Amad was assessed. We're still working on him, to get him ready for Sunday. Hopefully, it will work," said the club's interim head coach. "Kobbie is also progressing in his injury, he's making the right steps, but is not yet with the team, though. That needs a bit more time.
"I have to say, yesterday, we had a lot of benefit from Christian [Eriksen] playing 30 minutes, obviously [Manuel] Ugarte and Mason [Mount] making his first minutes again.
"That benefited us as well. So I'm glad that they're back and also, for a little bit longer [into the] future, good that Luke [Shaw] and Leny [Yoro] are on the pitch."
As it stands, Harry Maguire and Toby Collyer are the only senior Man United players not involved in training, and it is currently unclear when either will be available for selection again.