Williams is aware of the threat posed by Van Persie, but he believes Swansea have a plan to keep the Dutchman quiet on Sunday.
Wales captain Williams, who was named man of the match in last Sunday's defeat against Tottenham, is relishing the challenge of pitting his wits against Van Persie and feels the key to stopping him is to cut off his supply line.
"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.
"He's one of the best strikers in the Premier League if not the best. Technically he's very good and you can all see his goalscoring abilities.
"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."
United did the double over Swansea last season and Williams feels they showed too much respect to Sir Alex Ferguson's side last term at the Liberty Stadium when they lost 1-0.
However, Williams has promised things will be different this time and that Swansea will show no fear against the current Premier League leaders.
"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," added Williams.
"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."
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