The Kiwi heavyweight will fight in front of an exclusive live audience in a bout to help launch DAZN streaming service in New Zealand.
Manager David Higgins has been working on the event in conjunction with Parker's promoter, Matchroom Boxing boss Eddie Hearn.
At this stage, the most likely opponent is Lucas Browne, with the Australian able to take advantage of the proposed trans-Tasman bubble.
While talks of a potential clash with Junior Fa have heated up in recent weeks, Higgins insists the City Kickboxing product's asking price remains "unrealistic".
"Lucas Browne is a much bigger name than Junior Fa," Higgins told Newshub. "He's been in a sold-out O2 arena in London, has a profile in the UK and he's only had a couple of losses to very good opponents."
Another leading option is undefeated Queenslander Dempsey McKeen, an awkward southpaw from Queensland.
The Government's restriction on gatherings to 100 people in COVID-19 Alert Level 2 presents its challenge, but Higgins is adamant the event will only go ahead if they can guarantee safety, as well as financial viability.
"At this point we're optimistic and we're doing due diligence on running an event with less than 100 people, and how that could work on network television.
"It's a matter of the costs being less than the revenue and what that revenue looks like in this environment.
"We'll only pull the trigger if it's safe and economically viable. At this point, I'm reasonably confident."
Higgins stressed that any fighters or trainers involved would have to be assembled in Auckland for the entire eight-week camp and self-isolate accordingly.
No venue has been confirmed but Higgins sees an opportunity to host a more "intimate" event given the limitations on hand, and he isn't ruling anything out.
"We can be innovative here - it could be at an iconic location, it could be a marquee on someone's lawn. We're open minded."