The Red Devils will head to Palace sitting sixth in the table, two points clear of seventh-placed West Ham United, who travel to Brighton & Hove Albion, with the two teams battling for a spot in next season's Europa League.
Ralf Rangnick's squad has been hit with a number of fitness issues in recent weeks, but the 20-time English champions have been handed a triple boost ahead of the trip to Selhurst Park.
Shaw suffered a double leg fracture during a Champions League clash with PSV Eindhoven in 2015, and two metal bolts were placed in his leg during the operation.
The 26-year-old has since undergone surgery to have the bolts removed, and he was expected to be unavailable for selection until next season, having not been seen for the club since the start of April.
However, the England international was back training with his teammates on Tuesday, suggesting that he could be involved in the team's final match of the 2021-22 campaign.
Sancho, meanwhile, has not featured for Man United since the defeat at Arsenal on April 23, missing the last three league games against Chelsea, Brentford and Brighton through tonsillitis.
"Jadon might be out for the rest of the season with his tonsillitis. He will most likely be unavailable against Brentford," Rangnick told reporters earlier this month. "[It is] another three weeks to go against Crystal Palace. But for the next two games, I think it is unlikely [that Sancho will play].
"He's got inflammation on his tonsils and has also had some high temperatures so that's why he was not available tonight and he will most certainly not be available for the next two matches. Hopefully, they can get hold of that inflammation and if his tonsils have to be removed, that can happen at the end of the season."
The Englishman has scored five times and registered three assists in 38 appearances for Man United this term following a move from Borussia Dortmund, and he recently said that he is looking forward to 'a fresh start' under the club's new manager Erik ten Hag.
Like Shaw, Sancho was present at Tuesday's training session, while Rashford was also back on the grass, with the attacker missing out against Brighton due to bronchitis.
The 24-year-old has found it difficult to make his mark at club level this season, managing only five goals and two assists in 32 appearances in all competitions.
Rashford is widely expected to remain at Old Trafford this summer, though, with incoming head coach Ten Hag believed to be keen to help the attacker rediscover his top form.
Rangnick will discuss the state of his squad, in terms of injuries, at his press conference later this week, but Paul Pogba is expected to miss out once again due to a calf problem, meaning that he has more than likely played his final match for the club.
Man United could lose against Palace and still finish sixth if West Ham do not overcome Brighton, but a victory for the Hammers would leave the Red Devils needing to win at Selhurst Park due to their inferior goal difference.