A fourth shortlisted candidate, acting chief executive Alf Taylor, the council's education director, pulled out at the last minute.
Council leader Malcolm Glover said Mr Taylor, who has been acting chief executive since last May, had been 'absolutely brilliant' in the job and would have been the favourite.
He pulled out for personal reasons and is currently on leave from the council.
The three interviewed for the chief executive post were Bassetlaw DC chief executive Martin Havenhand, Manchester City Council deputy chief executive Patricia Coleman and Three Rivers DC chief executive Alastair Robertson.
Kirklees MBC executive director Annie Foulder was also shortlisted but withdrew earlier in the process.
Mr Glover said all the candidates were outstanding, capable candidates but following an intensive two days of interviews, 'we just didn't feel the right person was there, full stop'.
The panel has been very conscious of making sure it got the right person given Doncaster's special circumstances, Mr Glover said. The panel, which included Labour and Liberal Democrat members with outside consultants, decided unanimously to readvertise the post.
Liberal Democrat group leader Edwin Simpson said it had been a fair and open assessment of all candidates, and he shared the other members' disappointment that they had been unable to appoint someone.
Doncaster is still the focus of a police inquiry after a district audit report brought to light members' expenses abuses and questionable relationships between senior Labour members and local businesses.
Former finance director John Smith was singled out with Mr Hale for criticism by the auditor, and three senior officers were later suspended.
Consultants had been instructed to readvertise the post as soon as possible, Mr Glover said. It is a five-year contract with set performance targets and an£85,000 salary.