The Titans said they had given Bai permission to negotiate with other clubs for 2028 before November 1.
On the same day the NRL's 19th franchise unveiled their inaugural jersey and logo following a courtroom battle with Super Rugby Pacific's Waikato-based Chiefs, Bai travelled to the PNG capital to discuss his playing future.
The Titans confirmed in a statement that Bai's management had told them that he would not be extending his contract beyond next year.
Chiefs key signings Jarome Luai and Brian To'o also landed in Port Moresby on Wednesday with the Samoa side ahead of their World Cup showdown with the PNG Kumuls on Saturday.
Luai endorsed the Chiefs' pursuit of Bai.
"He is an amazing talent, and a young guy who has a long way to go and develop in his game," Luai said.
"He's Papua New Guinean. That is something I think will resonate with him, being back home amongst his people. So we will see how that goes."
Bai, who was ruled out of the Kumuls' World Cup campaign with a hamstring injury, will play his final season with the Titans in 2027.
"The family were coming for a holiday, so the Titans were good enough to give us permission to come and meet the Chiefs prior to November 1," Bai's agent, Anthony Field, told AAP.
"We thought we'd come a day earlier on the family holiday to visit and have a look and hear what they've got to say.
"He's got a contract for next year but, how 28 looks? We don't know. He (Bai) will come around, listen, hear it, see it, and feel it, and then he'll work it out."
Titans coach Josh Hannay said Bai had grown as a player in the past 12 months and, while "proud" to have played a role in his development, he was also excited about the club's talent coming through.
""We have some outstanding young middle forwards coming through, including Bodhi Sharpley, Viliami Fifita and Torino Jackson, who we believe can become key members of our squad in the coming seasons," Hannay said.
Last year Bai turned down the chance to sign with the Melbourne Storm - the club where his father Marcus made his name - which prompted a family fallout.
Marcus Bai is a member of the Chiefs' board and it is unclear whether he would retain that role if Cooper were to sign with the new club for 2028.
Bai jnr's signature would follow an impressive signing spree for the Chiefs. They have recruited Zac Lomax, Alex Johnston, Joey Manu, Connor Watson and Matty Lees among their seven inaugural signings.
The Chiefs are already flush with backline guns but Bai's signing would be a start in the right direction when it comes to attracting more forwards.
Luai said it was an aspect of recruitment he was sure Chiefs general manager of football Michael Chammas had "under control".
"November 1 is coming up, so we will see what it looks like," he said.
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