Jagoba Arrasate's side failed to take a single point from their opening three Group A fixtures, with the most recent of their defeats coming at the hands of United, who won 1-0 at Old Trafford last month thanks to Inigo Martinez's own goal after 69 seconds - the fastest own goal in Champions League history.
That came on the back of a 2-0 home defeat to Shakhtar Donetsk on matchday one and a 2-1 loss at Bayer Leverkusen a fortnight later.
Sociedad's elimination will be confirmed if they lose on Tuesday, or if they draw and Leverkusen win in Ukraine in the group's other fixture.
While they have struggled in Europe, Sociedad have prospered recently in La Liga, winning three and drawing one of their last four matches - including a 5-0 thumping of Osasuna on Saturday.
United, meanwhile, sit top of the pool undefeated with seven points from their three games thanks to a 4-2 home win over Leverkusen and a hard-fought 1-1 draw in Donetsk before their success over the Spaniards.
If United win it will be their first European away victory since November 7 last year, and manager David Moyes knows the fixture will not be a simple task for his side.
"It will be a difficult game in Sociedad," he said.
"To go and play any team in Spain who have qualified for the Champions League would be a hard test.
"We'll go there and hopefully try and get a result which can continue our good form in the group."
Their most recent visit to Spain came in last year's round of 16 when they drew 1-1 with Real Madrid before losing the home leg 2-1 and being eliminated.
Overall, United's away record against Spanish opposition is poor with just two wins, nine draws and 10 defeats from 21 matches.
Domestically, Moyes' side have improved in recent weeks after a shaky start, winning three and drawing one of their last four Premier League games. Saturday's 3-1 success at Fulham leaves them eighth, eight points adrift of leaders Arsenal.
After the game at Craven Cottage, Moyes admitted he had a number of injury worries ahead of the trip to Anoeta.
"Rafael looks as if he might be the biggest doubt, going over on his ankle," the Scot said.
"Tom (Cleverley) - hopefully the double vision will be okay in a day or two's time and Jonny (Evans), I couldn't tell you how his back would be."
