The Red Devils legends have tasted plenty of success at the 20-time English champions, who won the Premier League title at a canter last term.
Rooney has been linked with a move away from Old Trafford this summer, with Chelsea reported to have submitted a £20m bid for the England international.
But Cleverley revealed that Rooney – along with other established members of the United squad – are still desperate to win more trophies.
“The desire from Giggsy, Rio, Scholesy, Wazza… they’ve all won a number of titles and they’re still so hungry to win more,” Cleverley told United’s website.
“We follow on from that – it passes down to us and we want to be here in 10 years saying we’ve got six, seven or eight medals. You’re brought up like that at this club.
“We did really well last year. We didn’t just win it; we won it in style after the previous year, which really hurt us. We want to retain the title now. That victory parade was incredible and it makes us want to win more and more.”
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