The 20-year old has been mainly used as right-back in recent times (including two recent international caps with the Socceroos) but Southgate can see him flourishing through the midfield at the Riverside.
"There's an opportunity for Rhys. I thought he was one of our better players against Sheffield United," Southgate said.
"Obviously there are similarities between him and Matthew Bates, though I would say Rhys looks a little bit more composed in the position.
"He also offers a little more going forward.
"Rhys was a midfield player when he was a youngster so it's not a strange position for him.
"Matthew is very strong in the position, but Rhys made some fantastic tackles against Sheffield United and with his height, he can influence things in the air.
"If he continues to keep his game simple then he can make an impact there."
Williams says he would be comfortable in midfield despite being used more defensively by Australia coach Pim Verbeek.
"I've played in midfield loads when I was back at home but when I came here I didn't think I was good enough," he said.
"The standard was far higher here than in Australia - so I dropped to right back and concentrated on that.
"But I am happy to play in midfield. If that is what I am asked to do for the team then I'll do it. I am confident I can do a job there. And I am enjoying it there."