The England international was replaced at the interval of last weekend's 2-1 win over Aston Villa, with the substitution a precaution due to some pain that the defender was experiencing.
Shaw has been restricted to just 14 appearances this season due to injuries, and there had been fears after the Villa match that he could now be facing another spell out of action.
However, Ten Hag has said that the 28-year-old has a chance of being in the squad for Sunday's game at Luton, with Man United seeking to make it five straight wins in all competitions.
«Luke is doubtful for the weekend but we are positive he can make it. He came out as a precaution, it was the right direction. We work until Sunday,» Ten Hag told reporters during Thursday's press conference.
Ten Hag was also asked about the injury recoveries of Aaron Wan-Bissaka, Mason Mount and Tyrell Malacia, and the Dutchman admitted that the trio are still facing «weeks» out.
«Aaron Wan-Bissaka will take some weeks because he picked up another injury in training last week. Mason and Tyrell will take some more weeks,» he added.
«He had setbacks during his rehab process, it takes too long, it's bad for him, bad for us. But now we turned a point and it's positive and he will return soon on the pitch. It won't take long before he's returning in team training.»
Man United are also without Lisandro Martinez and Anthony Martial with long-term injuries, and the duo are likely to be unavailable for selection until the start of April.
Ten Hag was also asked about the challenge of playing at Luton's Kenilworth Road stadium
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