Piutau and Halai, who both have Tongan ancestry, want World Rugby to loosen the eligibility rules to allow capped players to return to tier-two nations.
An identical policy has been introduced in rugby league and the Daily Mail report that Nonu and Vito could also make themselves available for Samoa under the proposals.
"If there's a way to do it, I want to give something back and play for Tonga at the 2019 World Cup," Piutau told the Mail on Sunday.
Tonga are in the same pool as England for the World Cup.
"I have told the Tongan coach I would be on board if there's a way to do it," Piutau continued.
"If our sport followed the rugby league model, it would be a massive boost for the Pacific Islands and it would make the world stage competitive again.
"There's a lot of wasted talent. The rugby league boys put Tonga back on the map and union should do the same thing."
Piutau, 26, will become the highest paid rugby union player in the world when he joins Bristol next season for £1million per year.