Monk oversaw Swansea's victory against Aston Villa on Saturday.
Williams said: "For me Garry is the right man, I've said that all along.
"However, I'm not the one that has to make the decisions. I've seen what training's been like, the detail and how we've set-up. I said he should be given a chance and I still stand by that.
"He works ever so hard and we enjoy the meetings."