Hull's head of football operations Adam Pearson has promised supporters a "first-class" manager will be appointed at the club. Several names have been linked with the Championship outfit, including Eddie Howe, Paul Hart, Alan Curbishley, Gary Speed and Tony Mowbray.
Pearson refused to give any indication as to who would land the post, but revealed an appointment of the highest calibre would be made shortly.
"We're very happy with the way it's progressing and we're confident we'll have a first-class man in place very soon," Pearson told the Hull Daily Mail.
"We can't say anything more at this time. We're at a very sensitive stage but we're close.
"It's a confidential process but I hope people will understand why that's been the case when we come to announce a new manager."
Hull suffered relegation from the Premier League last season with crippling debts to the tune of £35m in close tow, meaning Brown's successor will have to work within a stringent budget.
Pearson said the new boss would possess plenty of experience. He added: "We're after somebody who's got a good track record in this division, someone with integrity and honesty."