It has been reported locally that Mr Morris is in negotiations with the council over a deal under which he would leave.
Northampton's response said only: 'The council has a policy that an individual's employment details are a matter between the council and the individual, irrespective of who that individual might be.'
Mr Morris has been in post for 18 years and is a former president of the Society of Local Authority Chief Executives & Senior Managers.
It did not say what the rating was, but one person close to the council said: 'No-one expects it to say anything other than 'poor'.'
Political control changed last May when a Labour administration was displaced by a minority Tory one. The council has imposed a 4.9% council tax increase after grappling with financial difficulties.
Tim Hadland (Con), cabinet member for financial strategy, said when introducing his budget proposal: 'When we took over the administration, the financial forecast for 2004-05 was based on a 6.2% increase in council tax, a 1.5% increase in government support, and a£1.7m spending gap.
'The government settlement means we have to find nearly£140,000 ourselves.'