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This week will be spent "fine-tuning the details face to face", according to Higgins, with the contest pitting Joshua's WBA and IBF belts against Parker's WBO crown. With Parker himself and other Duco Events staff expected to arrive on Thursday, signs are that the deal announcement is imminent.
Both fighters are undefeated: Joshua 20-0, all by stoppage; Parker 24-0, with 18 KOs.
Hearn told Telegraph Sport last weekend that The Principality Stadium in Cardiff on March 31 remains the front runner to host the fight - the same venue where Joshua defended his belts against late replacement Carlos Takam in October last year, earning more than £15million for his tenth round stoppage. Twickenham Stadium, at a later date, and other open air football stadiums are also in the running.
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Telegraph Sport understands that there is a chance that the fight contract may be made this week, but the venue itself may be finalised after further negotiation.
But Hearn did rule out the Nou Camp, Barcelona's football ground, as a possible venue with the idea having been mooted in the past fortnight.