The fact that the pair are seriously talking will boost the hopes of boxing fans who want to see Parker, 25, and 28-year-old Joshua in the ring together, and for Parker it will probably be a case of either Browne or Joshua in March.
If it's the former it will mean talks with Hearn have broken down, presumably to be resumed later in the year. Hearn has said he wants Joshua to fight three times next year, with Parker and American WBC world champion Deontay Wilder both in the mix.
Tyson Fury is promising a comeback too but will need to shift a considerable amount of weight in order before seriously thinking about getting back in the ring.
Parker has told the Herald he wants a credible challenge next against an opponent who will come to fight. If the Joshua fight isn't made, Browne, a heavily tattooed 38-year-old, fits the bill.
He is ranked the top heavyweight in Australia and has an undefeated professional record of 25 wins, 22 by way of knockout.
His most notable victory was against Ruslan Chagaev for the WBA world title in Grozny last year, following which he tested positive for performance-enhancing drugs and was stripped of his belt. He resumed following a suspension in May this year with a second-round knockout of journeyman American Matthew Greer.
For Browne to qualify as a voluntary defence for Parker he must rank in the WBO's top 15. He could achieve that by fighting for a regional belt under the organisation's banner.