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United currently sit fourth in the table behind Chelsea, Manchester City and Southampton, but their place is under threat after one win in five league games.
Sunday's 1-0 defeat to Southampton at Old Trafford saw United fail to register a single shot on target, and leaves them just a point ahead of Arsenal.
"My minimum objective this year is to qualify for next year's Champions League," he told Inside United – the club's official magazine.
"It would be great to pick up a European trophy with this club. That and a league title is what I really want to win."
Rojo's debut season in England has been interrupted by shoulder and thigh injuries, but he is close to a return and hopes to feature regularly from now until May.
He added: "Expectations from now to the end of the season, well, to try and give my absolute best in every game until the end, and hope that we pick up some good results along the way so we can be in with a shout in the shake-up for the title."
