Moon, who is out of contract, has been with the Rhinos since relocating from Salford in 2013.
The former Brisbane and New Zealand Warriors centre or stand-off is tipped to resume his career in the NRL once he returns home.
Moon has won two Challenge Cup finals, a League Leaders’ Shield and two Grand Final during his six seasons at Leeds.
The Titans have ruled out making a play for Moon despite being linked to the 30-year old.
“He’s not on our radar. We have done most of our recruiting for next year,”
Gold Coast chief executive Graham Annesley told The Gold Coast Bulletin.W
“We have got a few spots left, not for the high profile players but for those a bit further down our list.
“Tyrone was with us (in 2016-17) and was great around the club. He’s a good utility player, he can kick goals and will be a good back-up half for us.
“He’s had a great year in the UK and will be a great bonus for us.”