The Netherlands international has netted 12 times in 17 Premier League appearances and Williams is relishing the challenge of stopping Van Persie - and highlighted the need to stop the service to the ex-Arsenal man.
"Van Persie's on fire at the minute and playing with a lot of confidence so we just have to work to stop him and stop the service into him," Williams told the Daily Express.
"There's no doubt he's going to get a couple of chances, that's just the way it goes against a quality team, but we have to dominate possession and starve them.
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"He's a complete player and was one of the best I played against last season. You watch Manchester United so many times so you know what they're all about. But trying to stop them is a different thing altogether."
Williams believes the Swans showed Sir Alex Ferguson’s side too much respect when they lost 1-0 in last season’s match at the Liberty Stadium, but believes they can get a positive result this time around.
He added: "It is true that we showed United too much respect last season. We sat back too much in that first half and then got at them.
"We deserved a draw at least . Scott Sinclair missed a chance, an open goal, and they had one chance.
"But this season we've got a lot more belief. We don't fear anyone. We're at home and we've lost two on the bounce so it would be great going into Christmas to get a positive result."