The Pacific Games Council confirmed Tonga's withdrawal from hosting the event earlier this month, and asked for expressions of interest from "experienced" hosts.
Fiji and Papua New Guinea declined to make a bid with Samoa the only country confirming its desire to stage the games.
New Caledonia also ruled itself out, having last hosted the games six years ago.
Chief executive of the territory's Olympic Committee, Michel Quintin, said whoever does take on the hosting mantle needed strong financial backing.
"Because if you've got the money it will be more easy (but) if you've got to go and search the money before the games in two years it will be really difficult for them and for everyone," he said.
"I think it's really difficult because two years time is a really short time to organise a games but they've got all the equipment since (Samoa last hosted) the games back in 2007 so I hope and I feel that if they've got the games they will do a good games."
The Tahiti Olympic Committee is keen to bid for the 2019 Games, having missed out to Tonga and Solomon Islands in the initial voting process for the 2019 and 2023 events.
But last week the French Polynesian government announced it was against hosting the event because there was too little time to prepare.
Tahiti Olympic Committee president Tauhiti Nena said he would meet with the government this week in a final attempt to secure political support.
Michel Quintin said New Caledonia would support a bid from their fellow French territory, although it looked unlikely.
"The problem with Tahiti is they have no time to build new equipment so they could have finished some equipment but not to build some new ones," he said.
"That's not really good for them because when you bid for the Games it's to get new equipment so that's why the government didn't go with the (original request to support a) bid."
Photo: AFP A woman from the Tahiti delegation at the 2011 Pacific Games in New Caledonia