It comes after Australian Prime Minister Anthony Albanese wrote to British counterpart Keir Starmer to confirm his country's support of removal.
Mountbatten-Windsor was stripped of his titles by King Charles III last year and hasn't worked as a member of the royal family since 2019 over his ties to convicted sex offender Jeffrey Epstein.
However, he remained eighth in line to the throne.
The British government was considering passing a law to divest Mountbatten-Windsor of his succession rights after he was arrested by police last week, a UK official said.
But Seymour wouldn't be drawn into whether New Zealand would back the move, with more pressing priorities back home.
"I think we've got 99 problems most New Zealanders are facing right now," he told First Up.
"This guy's eighth in the line of succession, and these guys all seem to live to about 100.
"So, of all of the things that you could ask me about or we could be worried about right now, that's probably a wee way down the list."
Seymour said Australia had "obviously solved a few more problems" when quizzed if New Zealand had considered their position on the issue.
Good on them, he said.
