Manager David Higgins says a Kiwi showdown between Joseph Parker and Junior Fa could be confirmed in the next week.
The local rivalry goes back to their amateur days, when they fought four times, winning twice each, but they've never met at a professional level.
Fa is undefeated in 19 pro fights, while Parker's two defeats have come against Anthony Joshua and Dillian Whyte.
Parker has possible match-ups against Whyte, Alexander Povetkin, Dereck Chisora and Oleksandr Usyk on his radar, yet all four title contenders are currently busy.
Whyte and Povetkin are due to face off in Manchester on May 3 (NZ time), while the fight between Chisora and Usyk has been rescheduled for May 24. The latter fight was scheduled for March, but was delayed, after Usyk suffered a training injury.
Parker is coming off a knockout victory over American Shawndell Winters this month.
Higgins said Parker was eager to return to the ring, but would have to wait months for a fight against Whyte, Povetkin, Chisora or Usyk, making a bout against Fa the perfect match-up before a "big global name".
"Junior Fa and Parker would be huge in New Zealand, because of the local rivalry, but globally, the likes of Chisora, Povetkin, Usyk, Whyte would be bigger," Higgins told Sky Sports UK.
"Joseph Parker would happily fight any of them. Fa has got a decent record - I think he's ranked No.6 by the WBO - so if the others are tied up, it might make sense to fight Junior Fa and then move into one of those bigger global names next.
"Joseph won't shy away from any of them. He's champing at the bit to receive a formal notification of who's next, when and where.
"Joseph will fight anyone and he leaves that to the team, but he would gladly fight Junior Fa.
Junior has made a few comments publicly that have probably ruffled a few feathers, but Joseph is a genuinely humble guy and he would like to do his talking in the ring.
"If the opportunity presented itself, Joseph would love to show the world what he can do and put Junior Fa back in his place."
Earlier this week, Fa's manager, Mark Keddell, named his price for the fight.
"Junior wants that fight and we look forward to that fight," Keddell told Newshub.
"David Higgins has been on the phone to me a couple of times this week and we've let him know that Eddie Hearn needs to deal directly with Lou DiBella [Fa's US-based promoter].
"Yes, we want the fight, but let's make it worthwhile. Higgins has been on the record saying Parker is getting NZ$2 million a fight, so I look at the maths.
"When Joshua and Parker fought to unify the titles, Joshua brought two belts, Joe brought one - the split was 66 percent to 34 percent.
"So I look at No.2 in the WBO against N.6 and that's probably a 66-34 percent split.
"If Parker gets $2 million from a $3 million purse, 33-odd percent of that is NZ$1 million - that's what we want."