The Corrections Department has allowed Mr White to attend the meeting, but only in the capacity of mediator.
Affidavits from Watson, as well as from Mr White and Mr Hope, were filed with the High Court at Christchurch this week.
Mr Hope said he had no objection to Mr White being present to ensure the conversation was not misrepresented later.
"It's a meeting I've been wanting to have for many, many years and there are questions I've had in my mind that need to be asked," Mr Hope said.
"The only way to deal with that is have a face-to-face meeting with Mr Watson."
He had no issues with Watson asking to have a person present, just as he did not object to Watson's request to attend his mother's funeral in 2012.
"My desire is that if I can sit in there, in a controlled environment, and ask the questions, and establish that the answers being given are truthful and honest, it will be of some help to me."
Mr White told the Herald he "absolutely supports" the application and said he felt the Corrections Department's restrictions had been unreasonable.
"I mean, it's just a continuation of a three-year process. We first tried to arrange a visit between Scott Watson and Gerald Hope and myself back in 2013, and we've been continually denied and delayed and now restricted by Corrections."
He said it was "bizarre" that he was allowed, as a journalist, to interview Watson in prison last year yet still faced restrictions for this meeting.
"Really, nothing has changed for Scott Watson - his position is still the same, he remains in prison and convicted - all that's different in this instance is the father of one of the victims wants to attend the meeting."
Mr White believed the role of an independent third party to observe the meeting could - and should - not be provided by Corrections.
"If you can just imagine, this will be one of the most tense, and intense, meetings... between the father of someone who has been murdered and the man who has been accused of it, or has been convicted of it.
"And the possibility of miscommunication and misunderstanding exists there.
"After 18 years, and all of that tension that surrounds the meeting, I just think it's so obvious that you'd want to do everything you can to make the meeting transparent, to make sure there were no misunderstandings, and that there was an independent third party who could record it and could write about it if they want."
Asked if that's what he planned to do, Mr White said there was "always the possibility".
"That's something that obviously Scott Watson wants... it's one way that he can highlight his continued position that he's a victim of a miscarriage of justice and Gerald Hope is very open to [the meeting being reported].
"I make no commitment. I don't know what will go on in the meeting. I want the ability, as do the other parties, for it to be publicly recorded, but Corrections is stopping that."
In his magazine's own successful legal battle against the department to allow his interview with Watson, the costs to Crown Law alone amounted to more than $50,000, Mr White said.
"It's really been frustrating - it's just been one battle after another."
Vincent Arbuckle, of Corrections corporate services department, said Corrections was aware of the judicial review application.
"Mr White is free to make a separate request at a later stage to interview Mr Watson for an interview, as he has done in the past," he said.
"He is also free to interview Mr Hope on his experience after the meeting if both parties agree."
Corrections Minister Judith Collins would not comment about the case, including whether Corrections was right to refuse the meeting, as the matter was subject to a legal challenge.
In 2007, Mr Hope told the Herald he had growing doubts about whether Watson was guilty and would help fight to free the convicted killer if he was convinced of Watson's innocence.
In 2000 Watson's appeal to the Court of Appeal was unsuccessful and, in 2003, the Privy Council declined an application for leave to appeal.
In 2008 he applied to the Governor-General for a royal pardon, and a QC was appointed to re-interview key witnesses, but in 2013 his application was declined.
In December, North & South carried an interview with Watson, who told Mr White he did not know who Ms Hope and Mr Smart were.
"I've never met them, never seen them," he was reported as saying.
They definitely never came on my boat and I definitely didn't murder them.
"And they've basically dumped me in jail for half my lifetime, it must be coming up, for something I haven't done. It's destroyed my family and my life."
