West Papua has seen a low-level separatist war since Jakarta took over the former Dutch colony in the 1960s.
Solomon Islands prime minister Manasseh Sogavare made the proposal in Honiara this week to a ULMWP delegation led by their secretary general Octo Mote.
The memberships of both Indonesia and the ULMWP were the highlight of last year's MSG summit in Solomon Islands with the former securing associate membership and the latter observer status in the sub-regional Melanesian body.
Mr Sogavare says he believes it is important that the MSG engage Indonesia in dialogue with the ULMWP to gauge its thinking on the issues facing its Melanesian Papua region.
Meanwhile the ULMWP has indicated its desire to establish an office in Papua to further engagement with Indonesia and to try and do away with assertions from Jakarta that it only represents exiled Papuans living abroad.