Imanol Alguacil's side are currently top of Group E, three points ahead of second-placed Man United, with the two teams set to battle for first position this week.
Real Sociedad would claim first, and an automatic spot in the knockout round of the Europa League, providing that they avoid a two-goal defeat to Erik ten Hag's side.
The Basque outfit have won all five of their fixtures in the group stage, including a 1-0 success at Old Trafford in September, with Brais Mendez's controversial penalty securing all three points.
Real Sociedad recently went on an eight-game winning run in all competitions, while they have been victorious in nine of their last 11 matches.
However, Alguacil's side have now lost two of their last three, going down 1-0 to Real Valladolid in La Liga on October 22 before suffering a 2-0 defeat to Real Betis in the league on Saturday.
The White and Blues were missing a number of important players against Real Betis, and according to Diario Vasco, the team still have huge fitness problems ahead of this game.
The report claims that as many as seven players are expected to be absent, with Ander Barrenetxea, Mikel Oyarzabal, Aihen Munoz, Umar Sadiq, Momo Cho, Takefusa Kubo and David Silva set to miss out.
All seven allegedly were not involved in team training on Tuesday, and David Silva is the only one who has a chance of returning against the 20-time English champions.
Oyarzabal is still working his way back from a long-term knee injury, while Munoz has been on the sidelines since the middle of October due to a hamstring problem.
Barrenetxea has also been absent of late due to a muscular issue, while Sadiq and Cho have knee and hamstring problems respectively.
Kubo, meanwhile, is definitely out of this match due to a dislocated shoulder, but Alex Sola could recover from injury in time for the key European contest.
"I'm sure there will be a great atmosphere and we want to show the best version of ourselves to be able to score or win against one of the best teams in the world. It seems incredible that, with 15 points, we are not classified as finishing first in the group," Real Sociedad midfielder Mikel Merino told Marca ahead of the game.
Real Sociedad have another four games before the campaign breaks for the World Cup, following this fixture with league matches against Valencia and Sevilla, before taking on Cazalegas in the Copa del Rey.