Billiat's contract expires in June next year, meaning he can enter into pre-contract talks with rival teams in January if no fresh terms are penned.
With the in-demand playmaker keen to move overseas Downs risk losing him at the end of the season for free, having spent an estimated R8-million for his services from Ajax Cape Town in 2013.
"He has not signed anything with Sundowns," says Billiat's agent Siyabulela Loyilane.
"The deal is not close and is not far. Everything is on hold and the player is just chilling."
She also confirmed there was interest in the Zimbabwean from Saudi Arabia in the recent transfer window.
"There was interest but the deal fell through. He is now 27 years old and Khama deserves a good deal for his life in the next three years.
"There is no chance for a local team. If he doesn't get a deal overseas, he might as well remain with Sundowns."