"We have made an early start on discussions on a possible blockbuster in Auckland," Parker's manager David Higgins told the Herald today.
"David Tua v Shane Cameron remains a record breaker and hopefully this one would also capture the public's imagination.
"It makes a lot of sense. Junior is unbeaten and ranked No6 in the world by the WBO, while Joseph is ranked No2. A lot of people back Fa. Obviously as Joe's manager I think he would be the favourite, but Fa is a big unit."
Fa's manager Mark Keddell told the Herald: "We'd always be happy to do that fight. But the money would have to be right."
That could be a sticking point, added to which is the potential for the negotiations between Englishman Hearn, and American di Bella, to quickly break down. Entering meaningful discussions in an attempt to lock down a deal quickly appears to be the key.
Keddell, who suggested Fa would be happy for a similar share of the revenue that Parker enjoyed in his unification defeat to Anthony Joshua (about 34 per cent), added: "We have other options for the middle of the year, so Eddie is going to have to make a meaningful offer to Lou. I know they spoke a day after Joseph's fight in Texas."
Higgins confirmed: "We could make this fight happen next, but the numbers would have to work. There are other options on the table."
Asked whether he had been in talks with Dazn, a global sports broadcaster about to make its first start in New Zealand in May, Higgins replied: "Sky is the incumbent broadcaster. There have been no formal discussions with Dazn."
Parker is coming off an impressive knockout win against American Shawndell Winters in Frisco, near Dallas, and would relish locking in a fight against Fa in Auckland as many of his potential opponents are already locked into deals.
Dereck Chisora, Oleksandr Usyk, Dillian Whyte and Alexander Povetkin are all scheduled for fights in May or June. Other potential opponents include a rematch against Andy Ruiz Jr or a fight against Luis Ortiz, but neither match-up would be easy to make.
One potential other opponent is American Michael Hunter, a 31-year-old with a 18-1-1 professional record (his loss was to Usyk). After watching Parker's fifth-round knockout of Winters, Hunter called out the Kiwi, with his manager Martin Mikolajczak saying: "Parker is slow on his feet and his cardio is terrible. Michael would definitely KO Parker."
Fa, who has a 19-0 professional record, last fought in November - a points victory over American Devin Vargas in Salt Lake City. Parker has a 27-2 pro record.