Cleverley started 18 Premier League games last season as the Red Devils won their 20th top-flight crown but he could have even more midfield rivals next term.
“There’s always going to be world-class competition and this club’s always going to be linked with big players,” Cleverley told PA Sport.
“I don’t really take much notice of it – I just play my football.
“Sir Alex challenged us every day, so we were always having to impress him. It’s no different under David Moyes. We’re all working hard to impress.”
Cleverley scored two goals in 22 Premier League appearances last season.
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