Clark's "encourage" votes have slipped from 8 to 6, her "discourage" votes have increased from 5 to 8, and "no opinion" votes have gone from 2 to 1, according to Foreign Policy magazine.
Reuters and the magazine are both reporting that Guterres is still well ahead of the pack with 11 positive votes, two discourage and two no opinion.
Serbian candidate Vuk Jeremic has moved up to second (from fourth) and is now the highest placed candidate from Eastern Europe, the region which is favoured in the traditional rotational system.
The biggest movement has been in the position of Argentinian Susana Malcorra who has moved to third place from eight last time and is now the highest placed woman.
Slovenian Danilo Turk has slipped from second to fourth.
Bulgarian Irina Bokova who was third last time has slipped to fifth and Macedonian Srgjan Kerim has gone from fifth to sixth.
The results are never officially declared but usually leak quite quickly.
Croatian candidate Vesna Pusic withdrew her candidacy yesterday, reducing the field to 11.
Guterres was Prime Minister of Portugal from 1995 to 2002. Until last year, he was the UN High Commissioner for Refugees.
Vuk Jeremic was Foreign Minister of Serbia from 2007 to 2012 and has been president of the UN General Assembly.
Malcorra is Argentina's foreign minister and was chief of staff to current Secretary General Ban ki Moon.
Clark was Prime Minister of New Zealand from 1999 to 2008 and since then has lead the UN Development Programme.
Under the selection system, ballots are expected to continue until a consensus is reached.
None of the permanent five members of the Security Council, Britain, China, France, Russia or the United States, is exercising its veto at this stage.
