The midfielder impressed when earning his first cap during England's 2-1 success over Italy in a friendly international in Berne last night.
But inevitably many of the post match interviews focused on what Cleverley felt of Van Persie's expected switch from Arsenal to Old Trafford.
Cleverley said: "This is the first I've heard about but, if he comes, he will only strengthen us. He is an exciting player to link up with as a midfielder.
"He just adds to our goalscoring ability with Wellbeck, Rooney, Hernandez, Berbatov.
"I've admired him at Arsenal, he is a world class player, a goalscorer and is proven in the Premier League. All those three things will help us.
"I think Rooney and Van Persie were the top goalscorers in the Premier League last season and hopefully they can score as many this year."
England left-back Leighton Baines is relishing the prospect of facing Van Persie when Everton tackle United in Monday's Barclays Premier League clash at Goodison Park.
He said: "When you come up against United, if it's not a Rooney then it's going to be a Van Persie or a Nani.
"There is always someone else to worry about!
"The strength in depth these teams have is something you have to cope with.
"But I can't wait for the game. You always look forward to starting the season and it is great to be playing on a Monday against a team like United."
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Baines knows it is important Everton shake off their tag as slow starters.
He said: "It is important for us to get a decent start. It has always hampered and hindered us the last couple of seasons.
"There is no better game. We've always been at our best when we get after teams and when you play a team like United, that's what you've got to do.
"It's a good way for us to start the season."