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.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.