The non-self-governing states are colonized territories such as Montserrat (U K), U. S. Virgin Islands (USA) and New Caledonia (Fr). But there has been an issue, known as the Western Sahara conflict, where the Sahrawi people has been trying to get independence from Morocco in the last 43 years. Western Sahara is still not an independent country, therefore it will not be able to be a candidate for a place in UN.
And as a non-member state we have the Cook Islands and Niue, both located in the South Pacific Ocean, near New Zealand. Both territories are not already accepted as states because they are in a free association with New Zealand. "Free association is a status distinct from that of full independence in that it allows the Cook Islands to maintain New Zealand citizenship, while administering its own affairs." (New Zealand's government, 2013).