But Bokova, the head of the UN's cultural organisation Unesco, is widely expected to face a veto from the United States if she is short-listed.
Clark has also headed a UN organisation, the UN Development Programme, for the past seven years.
Two other women have held highly placed roles in the UN: Susanna Malcorra was Ban's chief of staff until becoming Foreign Minister in Argentina last year; and Christiana Figueres headed the UN Framework Convention on Climate Change.
Four of the top five candidates in the first ballot were from Eastern Europe, the favoured region for those who believe the position should be rotated geographically.
The vote will be held about 2am Saturday (NZ time) and the results are expected to be known publicly two or three hours after that.
The ballots are secret in terms of how countries have voted for which candidates.