At the time, Mourinho told the media that United had sealed all of their targets, but it is believed that the 53-year-old is now eyeing a top-level defender.
Bailly has been a welcome option at the back having helped keep four of United's seven clean sheets this season, but a knee ligament injury suffered in October halted his progress.
According to the Daily Record, Mourinho advised the board to sign a second central defender as well as a full-back in the summer, but neither materialised and now executive vice-chairman Ed Woodward is prepared to release funds for some big-money spending next month.
Injuries to Chris Smalling and Bailly have been felt by United as the club have conceded in their last three Premier League games.
Bailly's absence in particular has been a blow, and the Red Devils are expected to be without the Ivory Coast international in January as he is due to compete in the Africa Cup of Nations in Gabon.
If his nation reach the knockout rounds of the tournament, the defender will be away until February.