Van Persie completed his move from Arsenal on Friday and will enhance United's chances of winning the Premier League title this season.
De Gea said that he was forward to playing alongside the 29-year-old Dutchman even before the transfer was made official on Friday.
"He's one of the greatest strikers in the world and it would be a really great signing for us," the Spaniard told United's official website on Thursday.
"It's better to have him in our team and helping us. He's a player who scores a lot of goals and he's very cool up front. He has a lot of quality to his game."
United will begin their 2012-13 Premier League campaign with an away game against Everton on Monday.