Both camps are a long way apart but are likely to get closer, especially as New Zealand's coronavirus infections continue to drop while the opposite happens in the US and United Kingdom, the two strongholds of boxing – in a commercial sense anyway.
Parker's manager David Higgins' talks have so far been with Fa's New Zealand-based manager Mark Keddell, but he confirmed he had also recently been in touch with Fa's US-based promoter Lou DiBella.
Higgins told the Herald that Fa's team were being unrealistic in terms of money and that the opportunity was too good to pass up.
"New Zealand has handled this Covid-19 situation better than any other country," he said.
"For example, Trump's had a shocker in the US and they'll be closed for business for a while yet. We're in a bubble and while our borders are still locked down the fact is we have the WBO No 2 living in Auckland City [Parker] and the WBO No 6 living in Auckland City [Fa]. We're in a great position to make the first post-Covid global contest.
"I can confirm Joseph Parker has no problem fighting Junior Fa and we're told Junior wants this fight, but when the rubber hits the road the terms were so outrageous you have to wonder if he really wants to fight Joseph at all.
"They want US$500,000. That's about NZ$850,000. Joseph Parker was willing to fight for less than that and he's a former world champion. He's asking about double what David Tua and Shane Cameron got.
"The fight makes a lot of sense now for the reasons we have talked about and promoting it as the first big post-Covid global boxing contest. But if it doesn't happen Joseph will move on and start looking to Dillian Whyte and Oleksandr Usyk. You can't call out Joseph Parker to boost your own name and then price yourself out of the market.
"Everyone can win in this and make money. It could be exciting and groundbreaking but the only thing killing it is the ridiculous, outrageous financial demands. I would say greed, but it goes beyond that."
While Higgins' position is clear, so is Keddell's. He told the Herald: "You wouldn't sell your business if the future of your business was good, would you? We're not asking for anything unreasonable. If he [Higgins] can't afford to put the show on at the market rate, then don't put the show on. I understand that sponsorship is hard, I understand that corporate tables may not be easy to sell, but if you can't make that up with TV sales around the world - because everyone is at home - then that's on you. Don't make it the fighters' problem."
Those who remember the build-up to the Tua v Cameron domestic showdown in 2009 will know that this is likely to be the start of a long-running and entertaining saga.