"We have started those discussions and what we do in 2018 we are pretty open [about]."
According to Greenberg, it's also unlikely that the NRL would sign another five-year hosting deal, instead favouring rotating across different venues in shorter cycles.
"It's a great event that has got legs in a number of different markets," said Greenberg, "so we need to think carefully about what the next cycle looks like. Over the next three or four months we will have some conversations - not just about what 2018 looks like but what the future looks like as well."
"We've created a massively successful event so of course other parties are interested," said Duco CEO Dean Lonergan. "That's how it works. We are keeping an open mind and hopeful that is can stay here. That's the best-case scenario.
"But if it doesn't ... Duco would still like to be involved."
Though the Nines has its critics - and there has been a downward trend in crowd attendances since the explosive sell-out first year - the event has been important for the sport in New Zealand.
It helps to put the game on the map in February, draws all 16 NRL teams to Auckland and has also played an indirect role in the decline of the Wellington Sevens.
The future of the Nines in Auckland may be in doubt, but several top players think it would be a mistake to move the event.
"It has to stay in New Zealand," said Tigers captain and Kiwis international Elijah Taylor. "There is so much league in Australia: they've got State of Origin, grand final, finals series - I don't think they need the Nines.
"It might do well wherever it goes - but I am really hopeful it stays in New Zealand."
Cowboys co-captain Gavin Cooper, who lifted the Nines trophy in 2014, echoed Taylor's sentiments.
"I like the fact that it is over here due to the way that the crowd gets into it," said Cooper. "The way everyone embraces it, dresses up, has fun - the atmosphere that the fans create here is nothing like I have experienced in Australia. That would be a shame for it to leave."
And Ruben Wiki, who rolled back the years to lead the Warriors yesterday, was unequivocal.
"It shouldn't move," said Wiki. "It's vital to grow the game here in New Zealand and it gets great reviews. It needs to stay.
"For kids who want to play league it's massive that they get to see their heroes running around here. It would be silly to take it away."