"We think he's capable of a lot more than what a lot of other people think he's capable of," was the reply of Duco's Dean Lonergan when asked about the continued fast-tracking of Parker.
"It's not just a sole decision by me or [business partner] David Higgins. We take into account what our matchmaker Stuart Duncan has to say and most importantly we take into account what [trainer] Kevin Barry has to say. No opponent is secured without Barry's sign-off. He knows exactly where Joseph is at and we've passed a couple of names past Kevin and he said 'yeah, I like it'."
"I'm pretty excited about the steps we're making," said Parker. "I know I'm moving fast but to get better you have to keep fighting in the ring. My full concentration is on this week and Keith Thompson but I know we have other goals we want to achieve by the end of the year."
Lonergan refused to name possible opponents, but said Duco was looking at about five names.
One fighter not likely to be involved is Australian Lucas Browne, whom Lonergan said Duco had tried to match against Parker.
Undefeated Browne, 35, is rated as the 19th-best heavyweight in the world by boxing website Boxrec.
"Unfortunately we've entered into negotiations a few times and they want a ridiculous amount of money which is fascinating because they fight for four-fifths of nothing on cards overseas but see Joseph, at 22 years old, as a massive risk.
"I would like to think that by the end of this year Joseph would be ranked in the top five of at least the WBA and the WBO."
Sunday's fight against journeyman Thompson is unlikely to boost Parker's ranking, but fellow Kiwi Robert Berridge will be a big mover if he can defeat Russian Vasily Lepikhin on the same card.
"If Rob can win this then we have big things planned for later on this year as well. He is right up there and we want to keep pushing him."
Lonergan said he was still looking at venues for the Fight for Life event, a continuation of the popular series which will again be themed along union versus league. Auckland is unlikely to host it, with Lonergan saying he felt it was important for Parker to fight in a different part of the country.
There is a possibility that he will fight at Invercargill's ILT Stadium, which incorporates the velodrome, next year.
Patrick McKendry travelled to the US with assistance from Duco Events.