United enter the new campaign with no European football to look forward to - the second time in the club's history since English clubs were banned in the 1980s following the Heysel stadium tragedy.
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"Europe is a massive, massive thing for us," Mount said.
"The Champions League would be amazing for us and as a group we want to be playing in that competition.
"But I'd say Europe. I think that's the focus."
United finished in 15th place in the Premier League last season and lost the Europa League final to Tottenham.