Parker is unbeaten in his 23 professional fights with all but five victories coming by knockout.
The New Zealander had been due to face Fury in his hometown of Auckland on April 1 but his opponent pulled out citing an injury.
The fight was subsequently rescheduled and the pair will finally meet in the ring on Saturday night with the heavyweight title on the line.
But what are the latest odds and who are the bookies and punters favouring in the final few days before the bout?
Parker vs Fury odds: Who will win?
Fury would not even be the first man in his family to hold the title with cousin Tyson having won the WBO strap when he beat Wladimir Klitschko in 2015.
But he has since vacated the title and just as with that fight, with went to the judges, the bookmakers are clearly expecting a close bout as both boxers are unbeaten and neither have been tested by a world-class heavyweight before.
Betfair have the champion Parker favoured at 8/11 while Fury is only evens to take the belt.
Parker vs Fury odds: How will victory come?
The most popular bet so far has been Fury to win by knockout which is as long as 11/2.
However, the favoured method of victory remains Parker to stop the fight early – he is 15/8 to do so with rounds seven, eight and nine all priced shortest as 18/1 shots.
But if the fight does go the distance, Betfair seem to think it will be Fury who emerges victorious as he is 17/10 to take the win on the scorecards while Parker is out at 3/1.
That is despite three of Parker’s last five fights having gone the distance and the 25-year-old taking the decision every single time.