United host Anderlecht in the second leg of the Europa League quarter-final on Thursday and Young is hopeful that they can beat the Belgian side and advance in their quest to book a spot in next season's Champions League.
"We want to be pushing on. A lot has been said about how we want to finish fourth but... I want to finish higher than that," Young told British media.
"Hopefully we have a (Europa League) semi-final coming up. If we can play like we did against Chelsea, then I am sure we can get through against Anderlecht and into the semi-finals."
England manager Gareth Southgate was present during Sunday's match but Young remains focused on performing for his club rather than hoping for a call-up to the national squad.
"It is always an honour and maybe one day it (an England call-up) will happen again," Young said.
"But I am just concentrating on Manchester United and wanting to play well here. It is down to the England manager."
United travel to Burnley after the Anderlecht game before the Manchester derby on April 27.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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