A series of Premier League clubs have emerged as admirers of the player, with the likes of West Brom, Aston Villa, Bolton and Newcastle all being linked.
Middlesbrough boss Tony Mowbray has reiterated that Rhys Williams will not be leaving the club in January.
Mowbray has reinstated his desire to keep the Australian at the club.
“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.”
Meanwhile, Boro are close to completing the signing of Lukas Jutkiewicz on a permanent basis after he joined on an emergency loan.
However the Middlesbrough manager is eager to add to his squad.
“We’ve asked a few questions, we’ve made enquiries but things are never easy,” he said.
“The squad needs help, we’ve seen that with key injuries to key players a certain element comes out of our team.
“We’re working hard behind the scenes to help the existing group who’ve done so well to be where they are and hopefully we can do that before the end of the window.”