Van Persie was named PFA Player of the Year last season.
"He's one of the greatest strikers in the world and it would be a really great signing for us," De Gea told the club's official website.
"He made a great difference last year with the number of goals he scored. Our players will give him a lot of support and opportunities to score goals - so he'll soon find his rhythm and strengths here.
"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."