An appeal hearing was heard at the High Court in Auckland in March, with Justice Rebecca Edwards dismissing the appeal.
But name suppression has been allowed to continue up until May 3, allowing him and his legal team to seek leave to appeal to the Court of Appeal.
If the appeal is not filed, the man's name will be made public.
The former national representative was arrested after police executed a search warrant and took several people into custody in late 2019.
At his first appearance supporters in the public gallery called out reassurances to the man.
The maximum penalty on the charge of possession of a Class A drug, namely methamphetamine, is life imprisonment.
At the time, acting Detective Inspector Shaun Vickers confirmed Counties Manukau police had arrested two men after a joint investigation with Customs into methamphetamine supply.
The initial interim name suppression order, first granted by Judge John Macdonald, was extended on December 4, 2019, by Judge Peter Rollo to protect the ongoing police investigation.
On that day the accused appeared in a Manukau District Court dock alongside a co-accused and the pair were both remanded to appear in February 2020.
Both men were silent during the brief hearing, as their respective lawyers entered the not guilty pleas.
"They have each pleaded not guilty to serious charges before the court," Judge Rollo said.
A third man, connected to the case, appeared later in the Manukau District Court and was also granted interim name suppression.
He is also accused of importing methamphetamine.