The 27-year-old last featured for the Red Devils in their 4-0 defeat to Chelsea in October, while Shaw picked up an injury in his side's 4-1 win over West Ham United in the EFL Cup quarter-final clash. The left-back was replaced by Daley Blind after the break against the Hammers.
Shaw missed United's trip to Merseyside as they settled for a 1-1 draw against Everton. The Sun earlier reported that the England international will be fit to face the north London club on Sunday.
When asked whether Smalling and Shaw are fit to face Tottenham, the Portuguese tactician said, "not Sunday, no".
United summer signing Eric Bailly returned to the pitch after suffering a knee ligament injury against Chelsea. He played the full 90 minutes in the Red Devils' 2-0 win over Zorya Luhansk in the Europa League clash on Thursday (8 December).
However, the 20-time English champions will miss Bailly at the start of the year when he represents Ivory Coast at the African Cup of nations. Mourinho has admitted the centre-back's absence will be a "big loss" for United and remains hopeful that Smalling can make a comeback from injury during that period.
"Let's hope Smalling can recover in time to replace him in the squad because, with so many matches, we need players," Mourinho added.
"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," he said.
Henrikh Mkhitaryan is likely to retain his place in the starting lineup after scoring his first goal for United against Zorya. The Armenian international has now set his sights on scoring at Old Trafford.
David de Gea, Antonio Valencia and Michael Carrick were rested for the European fixture and the trio could return to the squad when they face Mauricio Pochettino's side. In addition to this, Wayne Rooney is also available for selection after the United captain served a one match suspension.