The 23-year-old, who is out of contract at the Riverside in the summer, has been linked with moves to West Bromwich Albion, Aston Villa and Newcastle United in recent days.
However, Mowbray is confident that the defender will extend his stay on Teeside.
"I'm pretty sure that anyone we don't want to lose won't be leaving," he said.
"Rhys Williams is not out of contract and talking to him the boy's pretty comfortable here so I don't see that being an issue.
"He wants to try and help us get back to the Premier League."
Williams joined Boro as a youth player in 2005.