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.