Hull City Council leader Steve Brady says a decision on whether to appoint a new chief executive at the Guildhall will be made within the next two weeks.
The search for a permanent replacement for Nicola Yates drew a blank recently when a panel of councillors decided against appointing anyone for the advertised £160,000-a-year post after interviewing two shortlisted candidates.
Councillor Brady said: "I will be recalling the appointments panel in the next fortnight to look at all possible angles and options. We have to bear in mind that, with a shrinking workforce and £50m being taken out of our budget over the next two years, the whole feel of the council is going to be very different in the future.
"For example, the proposals we have recently put forward for sport and leisure are a part of that. So I just think we need to sit down and think everything through very carefully with all the political groups, not just the Labour group on its own.
"We need to look collectively at the best way forward for the council. That could mean not going back out to recruit someone new or it could mean looking at the talent we already have in the organisation.
"What is certain is that we need a head of paid service because that is a legal requirement. Whether that will be a new chief executive or someone else, we shall have to wait and see.
"In the meantime, we have an excellent interim chief executive in Darryl Stephenson and I am absolutely certain he will continue to offer his advice and support."
Cllr Brady said the idea of extending Mr Stephenson's contract had not been discussed. It is due to expire in November.
He said: "There are experienced people around who we may look for guidance from and Darryl is certainly one of them. I just think it's now the right time to look very carefully at all the options before us and not rush into anything."
Ms Yates abruptly left the council 14 months ago after being in charge for nearly three years.
No official explanation was given for her sudden departure.
However, Guildhall sources claimed her exit was triggered by a breakdown in working relations between her and the recently elected ruling Labour group.
The post of chief executive at the council was advertised in the local government media in July.
At the time, the advert for the job said: "We want a dynamic chief executive who shares our pride, will work with elected members to drive our transformation agenda and re-establish the city in its rightful place in the premier league."
The successful applicant was also expected to be a "an inspirational, motivational, enthusing leader and corporate player".
The advertised £160,000 salary matched Ms Yates's pay after she took a £40,000 pay cut on appointment in 2009.
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