The diplomats declined to be named because the process is sensitive and ongoing.
Unconfirmed reports suggest Nouri Abu-Sahmain, head of Tripoli parliament, and Khalifa Ghweil, prime minister of Tripoli Salvation government, could be in the EU`s sights.
Libya has been split between rival governments since 2014, a consequence of the chaos that engulfed the country after a 2011 uprising that toppled and killed longtime dictator Moammar Gadhafi.
EU foreign ministers will hold informal talks on Libya in Brussels on Monday.
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