Parker recently saw off mandatory challenger Hughie Fury in Manchester and is allowed a voluntary under the World Boxing Organisation rules.
After initially considering a fight in Japan against Kyotaro Fujimoto this December, Higgins says a deal with Browne could delay a planned return to action for Parker before the end of the year.
“Bob Arum has mentioned a possible bout in the US in February and also Lucas Browne’s people are talking to us about a big Trans-Tasman affair,” Higgins told RadioLIVE.
“It would probably make sense in Auckland or New Zealand because Joe has a better fan base in New Zealand than Browne has in Australia so you could mount a big Trans-Tasman clash.
“Browne would have to be ranked by the WBO first but that could be possible so looking at December, maybe February which is a possibility.
“Joseph has a good profile in Australia because we gave away two or three of his fights for free to Fox Sports and they put him on their free channel.
“His last fight was put on Pay Per View and it didn’t do too bad. I was surprised how well it did – It wasn’t massive but a decent amount of people got up to watch the fight which is encouraging.”
On the possibility of giving Fujimoto a shot, Higgins added: “I have had multiple emails and there a few conversations underway and that is the best way for it to be because you want to create some competition so you can get the best deal possible.
“We’d make history because no Japanese heavyweight has ever fought for the heavyweight title and Japan is like the second biggest economy in the world.
“It is attractive to broaden Joseph’s appeal and profile around the world and to go to an Asian centre would be great.
“It is a similar time zone to New Zealand and Australia for TV and so it really comes down to what the deal looks like and we have got discussions underway, but that is not the only discussion which is underway.
“It is about making money, but not only getting the money it is about expanding profile as well,” he added.
A fight with the winner of the Tony Bellew v David Haye rematch is still high on the agenda for Higgins, although any fight with Browne could potentially push that encounter back until the summer.