Smalling has not featured for United since the 4-0 defeat at the hands of Chelsea back in October due to a foot injury, while Shaw is struggling with minor physical discomfort that kept him out of the Europa League win over Zorya on Thursday and the draw with Everton last weekend.
United were initially hopeful the duo could return versus Tottenham, but Jose Mourinho has made it clear both defenders are not ready yet.
"Not Sunday, no," Mourinho told reporters when asked about a potential return for the duo.
Fellow defender Eric Bailly recently made his comeback from a knee injury, but the defender will be unavailable next month when he will represent Ivory Coast at the Africa Cup of Nations, much to the disappointment of Mourinho.
"Bailly's absence will be a huge loss," he admitted. "Let's hope Smalling can recover in time to replace him in the squad because, with so many matches, we need players.
"At the moment, we have Phil Jones, Bailly and Marcos Rojo [as centre-backs].
"We play Tottenham, West Brom and Reading, West Ham away [among others] - in that period we have a lot of matches and it is important to have players."