The decision is being seen as the first big test of the new organisation - formed from the merger of the Colleges' Employers' Forum and the Association of Colleges. Many principals feel the body, provisionally called the Association of British Colleges, must prove its independence from its parents to get cross-sector support.
They believe other candidates must be considered for the post as well as the CEFand AFC chief executives.
Both sides in the merger are claiming to be jubilant over the board election result, which saw all 12 principals and chairs of governors on the CEF slate elected.
CEF chief executive Roger Ward is claiming a landslide, while Association for Colleges counterpart Ruth Gee insists the split between major supporters of the two merged organisations is 60:40 in the CEF's favour.
Some of the new board members drawn from the old CEF board are understood to want to see Mr Ward appointed chief executive immediately on their inaugural meeting on Tuesday.
But they have been dissuaded by fellow members and by Mr Ward himself who knows his standing would be greater if he were seen to win through open competition.
Board member Michael Blagden, principal of Southgate College, said he expected the board to be unanimously in favour of an advertisement.
Mike Austin, former AFC president, is calling for the appointment of an external assessor to oversee the appointment. He said: "That will reassure people who might not particularly like the result."
However, the new organisation is unlikely to be able to put a new chief executive in place until September, and the board will have to move swiftly next week to decide on interim measures.
Mr Blagden has asked lawyers Eversheds, who act for the AFC and CEF, to draw up options. They are expected to include appointing one or both of the current chief executives to steer the new organisation in its crucial first weeks.
Ms Gee said: "I presume that Roger and I will be jointly interim chief executives. That is the only fair and equitable thing to do."
The board will also have to set subscription levels and decide on a final name. Mr Ward proposes calling the new body the Association for Colleges "as a gesture towards bringing the old and new cultures together".
Others being tipped as possible chief executives are Keith Scribbins, former CEF board chairman, Roger McClure, Further Education Funding Council finance director, and Colin Flint, principal of Solihull College. None would be likely to apply unless they felt certain of winning the job.
Moderate governor representatives on the new board said they were anxious that the new body should be seen to have broken away from its two parents.
David Kissman, the Broxtowe College chairman of governors named on both slates, said: "The fact that a lot of the CEF slate got elected should not mean that this is the CEF reborn."
Insiders believe colleges may have been swayed to favour the tough CEF style when voting by fear over impending funding cuts.
But principals want the new body to move forward without delay. Ken Ruddiman, of Sheffield College, said: "The elections were fair. The sector has spoken and there is nothing devious to indicate this is not a fair reflection of its views. Now the sniping must stop and we have got to put forward a common voice to the Government to stop the rot."