If Jai Arrow signs with the Rabbitohs, the Titans will not let him go until the 2021 season, according to The Sydney Morning Herald.
Gold Coast remain hopeful that the forward will accept their revised three-year offer, with club boss Dennis Watt expecting an answer next week.
Souths want the 24-year old to Redfern next year to help fill the void by retired star Sam Burgess and brother George to the Super League.
"Our focus is on retaining Jai and extending his contract, and [releasing him early] is not something we'll consider," Watt said. "Jai is rock solid. He's a real asset to this club, the game and the Gold Coast community.
"We are hopeful things will be resolved by next week. We think a decision is imminent.
"We've been respectful of Jai and his management. Him leaving early is not even a consideration for us. We're focused on extending his tenure, that's our priority."
South Sydney coach Wayne Bennett came out and declared he would like to be re-united with Arrow, having worked with him in the past.
Arrow has also been linked to the Wests Tigers.