Currently, the built-in interlanguage links list shows the language's autonyms. The same happens with compact language links.

In both of the above cases, the name in the user's language can be seen in a tooltip, but this is not convenient for somebody who want to see all of them at once.

Showing the language name as an autonym makes general for most people. This is what happens in language selectors in most websites and operating systems. For example, you cannot expect a German speaker who doesn't know Russian to be able to find the name of German (немецкий) if it is only shown in Russian.

However, Wikipedias is some languages have gadgets that show the language names. For example, the English Wikipedia has "SidebarTranslate" and the Portuguese Wikipedia has "Tradução Interwiki", and they are enabled by many editors, so this must be useful for at least some people. Similar requests were also made by the participants of the discussion about Compact Language Links in the German Wikipedia.

Making it available to more people as a proper MediaWiki feature rather than a gadget is worth exploring, but it will require proper design work, with definition of audience, testing, and so on. This is just a proposal.