Sneijder, 26, enjoyed a hugely successful season at club level after leaving Real Madrid for Inter Milan last summer, and he has now proved one of the stars of the 2010 World Cup.
Inter president Massimo Moratti has said he believes there is truth to rumours United are readying a bid for Sneijder, and Robben believes a move is likely to go through.
"Sneijder for me is the best player in the world over the last 12 months," he told the Daily Star Sunday. "Messi is clearly a fantastic talent but it's almost too easy to say he is the best now.
"I personally think there is a very good chance he will join Man United. I am a big admirer of Paul Scholes, he is one of the best players of his generation and I honestly think Sneijder is the only player in the world capable of replacing him."
Sir Alex Ferguson has played down the talk of a deal to sign Sneijder. He told the Mail on Sunday: "I believe the squad is stronger than last season with the younger players having another year under their belts. I don't know where those reports about Sneijder came from. How can anybody turn me down when I haven't even made a bid?"