A clause in Klese's contract could allow that to happen as soon as 2027.
Last October, the Titans announced 23-year-old Klese had re-signed until the end of 2027 on a three-year deal.
However, his agent Ahmad Merhi - who also manages Payne - told AAP an option existed for the final year that allows Klese to become a free agent.
"The only thing Payne has ever asked of me is that he would love to play with his brother. That's it," Merhi told AAP."That could definitely happen. Klese has got a clause in his contract in his favour.
"He has a three-year deal with the Titans but he has got until October to decide whether he wants to be there for three years or just stay until the end of next year. If he takes up that clause, then he is off contract the same time as Payne (at the end of 2026).
"They would love to play with each other. Any siblings are like that. I look after the May brothers and they are the same. It's a normal thing."
Merhi said that the clause was put in place to look after Klese's interests long-term.
While the Broncos appear the most likely club where the duo would play together, that scenario might not be straightforward.
"The whole purpose of that clause wasn't put in place for Payne and Klese to play together. It was all about Klese's performance and how much he is getting paid," Merhi said.
"They want to play together but is it going to happen? The only way it is going to happen is if Klese is getting his correct value. He's not going to take pay cuts to play with his brother."
Payne and Klese have only played against each other once in the NRL, in Gold Coast's 36-34 win at Suncorp Stadium last year. That is the venue for Saturday night's clash between the two struggling sides.
"I'm one up against Payne, so hopefully I keep that streak going," Klese said on Monday.
Gold Coast are in last place after losing seven of their past eight, including a 28-16 defeat to Melbourne last week where they had at times looked a live chance of winning.
The heat is on coach Des Hasler but Klese said the Titans players enjoyed his mentorship.
"Honestly, I feel like we can take a lot out of (the Storm loss). We were right in it," he said.
"It's just that five minute period before halftime that screwed us, but if we just get our minor details right, then we'll be sweet.
"We're strong behind Des. Fix up a few minor details and we're one of the best teams in the comp."
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