Despite a series of spluttering performances at Old Trafford, Mourinho's men are unbeaten in their last 22 league games.
With leaders Chelsea and second placed Tottenham clashing in the FA Cup semi-finals, the fight for Premier League supremacy is on hold until next week, but there is still plenty at stake in this weekend's fixtures.
Significantly, the other FA Cup semi-final features Arsenal and Manchester City and their leave of absence in the league means United have a golden opportunity to close the gap on the top four.
Jose Mourinho's fifth placed side breathed new life into their Champions League push with an impressive 2-0 victory over Chelsea last weekend and a win at Burnley on Sunday would leave them only one point behind fourth placed City.
Despite a series of spluttering performances at Old Trafford, Mourinho's men are unbeaten in their last 22 league games and United winger Young is confident a return to Europe's elite club competition after a one-year absence is well within their reach.
They can also reach that goal by winning the Europa League after making the semi-finals on Thursday.
"I don't think a lot of people saw that scoreline against Chelsea coming or the type of game to be honest. We did," Young said.
"We have belief in ourselves. I have confidence in every single player. There is great competition in the squad.
"A lot has been said about how we want to finish fourth but I am that kind of person who wants to achieve more than that. I want to finish higher than that."
Liverpool are one of the teams United hope to catch, but their bitter rivals show no signs of slipping despite a growing injury list.
Fuelled by the superb form of Philippe Coutinho and Roberto Firmino, Jurgen Klopp's third placed side have won five times during a seven-match unbeaten run.
A victory over resurgent Crystal Palace at Anfield on Sunday would allow Liverpool to retain at least a six-point lead over fifth place.
It would also improve their chances of finishing in the top three, which brings qualification for the Champions League group stage, instead of the play-off early next season that awaits the team in fourth.
As well as Coutinho and Firmino have played, Liverpool have also been indebted to Belgian goalkeeper Simon Mignolet, who kept his first clean sheet in almost two months in last weekend's 1-0 win at West Bromwich Albion.
"The last few performances against these teams like Burnley, Stoke and West Brom, we need to learn from that," Mignolet said.
"To be resilient, and to grind a result out, that's what we did, and I think everybody is pleased with that."
At the other end of the table, there will be plenty of nerve-jangling moments as Middlesbrough, Hull, Swansea and Bournemouth battle to avoid relegation.
Second bottom Middlesbrough are six points from safety and without a win in 16 games as they head to Bournemouth, who are seven points above the bottom three.
"We have to keep believing and keep the chin up. This is the toughest league there is, but we will keep grafting," Middlesbrough midfielder Adam Clayton said.
"The gap hasn't been getting any bigger, but now we are getting to the stage where we need to win. If we don't, it will be goodnight."
Time is also running out for third bottom Swansea, who host Stoke on Saturday, after five defeats in their last six matches left them two points from safety.
Fernando Llorente, Swansea's leading scorer, said: "We have done well at the Liberty Stadium and we have to do that again now.
"The game against Stoke is a massive match and we have to win."
Hull, two points above Swansea but beaten in their last two games, would do their survival hopes a power of good if they beat Watford at the KCOM Stadium.
Fixtures (1400 GMT unless stated)
Bournemouth v Middlesbrough, Hull v Watford, Swansea v Stoke, West Ham v Everton
Burnley v Manchester United (1315 GMT), Liverpool v Crystal Palace (1530 GMT)