Williams signed for the Perpignan club in June until the end of the 2014 season, after slipping down the pecking order at St George-Illawarra Dragons.
“I was in and out of first grade, and the Dragons signed Benji Marshall. Obviously that put me back,” Williams told Beinsports.fr.
“Everything about the club has been really positive. I’m really excited about the potential to stay long-term.
“I guess this season will tell me a little more about where it’s all at, but I’d love to be able to stay.
“It’s always something I wanted to do, and whether it’s this stint or a shorter one or a longer one, I’m very lucky to be able to come over here and do it.”
Williams made his first start for the Catalans in last weekend’s narrow defeat to Leeds, partnering Leon Pryce in the halves.
He made his debut for the club the previous week from the bench at hooker. He is happy to play in any position, however, as long as he is on the pitch.
“Halfback or five-eighth are the main positions that I’ve played,” he explained.
“I’m happy anywhere, I honestly don’t mind, as long as I’m on the field, I’ll play anywhere.”