While Everton have the same ambitions, Carlo Ancelotti's side sit in 11th place and five points adrift of their next opponents.
Although there have been times this season when Ole Gunnar Solskjaer has looked close to the sack, club officials will currently be relieved that they showed faith in the United legend after a disappointing run of results.
While United sit just outside of the top four, three successive wins and clean sheets in the Premier League have left supporters feeling optimistic about the future.
Silverware also remains a possibility after Thursday's 5-0 demolition of Club Brugge in the Europa League - a result which has taken United into the last 16 of the competition.
The English giants have now put together a seven-match undefeated streak since since January 26 - something which Solskjaer will want to extend as the games continue to come every few days.
Despite plenty of players chipping in with important performances, the influence of Bruno Fernandes since his January arrival cannot be exaggerated.
Two goals - both from the penalty spot - and two assists have come from his five appearances, but it is the 25-year-old's general presence and desire to create which have led to him already becoming a crowd favourite.
At the other end of the pitch, Eric Bailly is effectively regarded as a new signing, and his first two performances since recovering from a serious knee injury will surely convince United to hand the Ivorian a new contract in the coming months.
With Manchester City, Tottenham Hotspur and Sheffield United to come after the trip to Merseyside, Solskjaer will not be getting carried away with his team's recent revival, but the signs are there that everything is in place for United to end the season on a high.
As far as Everton are concerned, Carlo Ancelotti is likely to still be frustrated after witnessing his team concede three sloppy goals in defeat at Arsenal last weekend.
The result has led to the Toffees dropping down to 11th position in the table, despite having collected 11 points from their previous five outings in the top flight.
Nevertheless, the missed opportunity at the Emirates Stadium may ultimately work in their favour, adding motivation to the squad for the upcoming meetings with United and Chelsea.
Ancelotti will feel that their fate is still in their own hands, with victories against both of their rivals potentially being enough to earn a place in the top six.
With just eight points separating fourth and 11th, the margins for error are small, but a certain degree of pressure has been lifted from Everton ahead of one of their most anticipated fixtures of the season.
After five games without a clean sheet, their defensive performance will be under the spotlight, although United will fear what Everton are able to offer at the other end of the pitch.
Despite the perception that Everton are overly-reliant on their front two, it has taken a team effort to improve the club's standing in the table, and Ancelotti will be confident that their recent setback will only galvanise his squad going forward.
Everton Premier League form: WDDWWL
Manchester United Premier League form: WLLDWW
Manchester United form (all competitions): WDWDWW
Although Solskjaer has plenty of options with regards to his formation, the Norwegian has made a habit of using a back three against the better teams on away soil.
Fernandes should play as the most advanced of a midfield three, with Luke Shaw getting the nod on the left-hand side of defence.
Despite the disappointment at the Emirates Stadium, Ancelotti is unlikely to make sweeping changes to his team for this match.
Everton possible starting lineup:
Pickford; Coleman, Mina, Holgate, Digne; Iwobi, Gomes, Delph, Sigurdsson; Richarlison, Calvert-Lewin
Manchester United possible starting lineup:
De Gea; Lindelof, Maguire, Shaw; Wan-Bissaka, McTominay, Matic, Williams; Fernandes; Greenwood, Ighalo
Head To Head
Sunday's encounter will represent the 203rd competitive fixture between the two clubs, with United recording 88 wins in comparison to 70 victories for Everton.
Despite United's historical advantage, Everton have fared better in recent games, avoiding defeat in both of the matches which were played in 2019.
After thrashing United by a 4-0 scoreline at Goodison Park in April, the Toffees gained a share of the spoils at Old Trafford earlier this season.
We say: Everton 1-2 Manchester United
While Everton will be motivated to get the better of their North-West rivals, we are backing United to continue their recent form with a hard-fought win. The visitors are capable of keeping yet another shutout, although Everton are scoring plenty of goals under Ancelotti.