The England international has missed his team's last four matches in all competitions, having suffered a head injury during the 4-1 defeat to Watford on November 20.
Shaw was also expected to be on the sidelines for Wednesday's European fixture with Young Boys, but Rangnick has suggested that the left-back could make his return against the Swiss outfit.
"Aaron [Wan-Bissaka] can play, hopefully even Luke Shaw will be available for the game. Nemanja [Matic] will be captain tomorrow. Juan Mata will get game-time, Jesse Lingard. We have quite a few players who will be playing who definitely desperately need game-time," Rangnick told MUTV.
Shaw's absence has opened the door for Alex Telles to feature at left-back, and the Brazilian appears to have moved ahead of the former in the pecking order under Rangnick.
Dean Henderson, Donny van de Beek and Nemanja Matic have also been confirmed as definite starters for the 20-time English champions on Wednesday, with the Red Devils already booking their spot in the last-16 stage of the competition as Group F winners.