United's medical staff had hoped that rehabilitation in Manchester would avoid the need for surgery but the manager revealed in midweek that time was running out on that option. That suggests Marcos Rojo (head) and Marouane Fellaini (knee) will be absent again.
The pair are understood to have fallen out with Mourinho and are set to be offloaded in January.
If City were to drop points against the resurgent Lilywhites, United could trim the gap at the Premier League summit by beating West Brom the next day.
Mourinho and Willian worked alongside each other during the former's second spell in charge of Chelsea, and the Portuguese gaffer got the best out of his star during his time at the helm.
Mourinho said: "When I went to Real Madrid, they were in a hard moment, no league title or cup, not even a Champions League quarter final for many years".
Blues boss Antonio Conte is keen to keep his squad intact for the second half of the season, and would not want to see one of his players join a club which is likely to be challenging them to see who finishes second in the league behind Manchester City.
The Armenian started the season in fine form, assisting five times in the opening three Premier League games of the season. I had that experience before.
"We go to clubs with a huge history where people look to the history and not to the moment and expectations are high".
Jose went on to say in his press conference ahead of the match against West Bromwich Albion that if an opportunity arises in buying someone in the winter transfer window, he will go ahead. "I'm not a big defender of the January market but there are players and situations that sometimes you have the chance to do and you shouldn't lose that chance".