Reports suggest the fight will take place on March 31 at Cardiff's Principality Stadium, which staged Joshua's most recent victory against the French challenger Carlos Takam.
Joshua is expected to come face to face with the New Zealander next week, provided that talks go to plan, and they will resume a verbal battle which was sparked by a string of critical comments from Parker and Higgins.
Duco are sending a small team, alongside Parker, to follow promoter David Higgins - who flew to London earlier this week to meet face-to-face with Joshua's handler Eddie Hearn.
"Joshua is a big man".
"We're excited about Joshua", Higgins told Behind the Gloves.
"We need these belts, there is no secret, and they know that as well", he said.
For a quiet man not prone to bouts of trash-talking, Joseph Parker offered a dramatic message of intent yesterday as the World Boxing Organisation heavyweight champion revealed his "sole mission is to smash to bits the man with the glass chin".
Talks have been quite amicable, meaning Parker was happy enough to make the long trip to the United Kingdom to take part in a press conference to confirm the fight early next week.