Negotiations for a fight between former world champion Parker and the top-10 ranked Fa stalled once again early last month.
But the all-Kiwi contest was again being lined up.
Parker's British promoter Eddie Hearn revealed on Thursday details were being finalised for a big fight in New Zealand in October.
Responding to Hearn's comments, Parker's manager David Higgins confirmed discussions were advancing and revealed Fa was still their preferred opponent.
"All the key parties - Junior Fa, Joseph Parker, Lou DiBella (Fa's promoter), Eddie Hearn - everyone wants to see if we can make it happen.
"October is a bit optimistic now, given the limited time left and the latest Covid outbreak, so it's more likely to be [after that but] before Christmas."
A potential fight between Parker and Fa had been bubbling away for some time now.
Parker (27-2) was trying to get back into title contention and had reached No 2 in the WBO rankings, while Fa (19-0) had risen to No 6 with the same organisation.
The pair are also both from Auckland and have history at amateur level, each winning two of their four fights.
Disagreements over the financial split scuppered the most recent attempts to get the bout done but Higgins said the two parties had well and truly resumed discussions to settle on the numbers.
"We've indicated slightly more money their way, and then there's been a few concessions the other way.
"Without getting into detail, talks are ongoing but there's still a gap. We're not there yet."
While Fa is the Parker camp's preferred opponent, Higgins said the cagey nature of negotiations so far meant other options were being considered.
He said all their alternatives were overseas fighters and they were investigating what was possible with border exemptions.
"We've had a look at what the process is.
"Although right now, given that we're going to give ourselves a bit more time, we might wait and see what the government decides to do in terms of other sports and what precedents are set in terms of what's allowed and what the processes are."
The first two bouts of Parker's three-fight deal with Hearn's Matchroom Boxing have been in the United States, the last of which was a fifth-round TKO of American Shawndell Winters in February.
Parker last fought in New Zealand in December, 2018.
Fa's last fight was a unanimous decision win in Utah in December last year.