The equation is simple for second-placed United, who need to win their last two games and hope Manchester City falter if they are to clinch a record 20th English league title.
United were edged out 1-0 away to City on Monday and are now equal on 83 points with their local rivals. City, however, boast a superior goal difference of plus eight.
United will host Swansea before travelling to Sunderland for their final game, while City face Newcastle away and Queens Park Rangers at home.
United striker Danny Welbeck is in doubt for both fixtures after he was felled by a Nigel de Jong challenge in the closing stages of the Manchester derby.
Welbeck was cleared of serious injury but the knock may force United manager Sir Alex Ferguson to turn to Mexican forward Javier Hernandez, or hand a potential recall to England international Michael Owen.
Promoted Swansea, in 12th place on 44 points, mathematically secured their Premier League status for next season with a 4-4 draw at home to Wolverhampton on Sunday.
City manager Roberto Mancini suggested Swansea will be an 'easy' task for United, but Icelandic midfielder Gylfi Sigurdsson refused to buy into the comment.
"I'm sure it's just a bit of mind games going on," Sigurdsson told WalesOnline.co.uk.
"We can't worry about that, we will just train hard and look to get something from the game like every game we go into.
"Everyone knows it's a huge game for them but it's a game we want to do well in and perform in.
"It is the biggest club ground in Britain and any player would want to go there and put in a performance.
"When I came over here it was a game I looked for and it'll be fantastic to play at Old Trafford."
Swansea have won just one of their last seven starts, while United are looking to bounce back from a 4-4 home draw in their last appearance at Old Trafford.
soccerway.com