Relatives of those who died at the hospital have been placing pressure on the Prime Minister to sack Sir David, who was the head of the Trusts' Regional Health Authority at the time.
Speaking last night in India, Mr Cameron said Sir David was doing "a very good job".
"I would remind you of what the report says, that we should not be seeking scapegoats. I think to highlight David Nicholson in that way would be seeking a scapegoat."
A public inquiry has blamed a failure 'at every level' of the NHS for the abuses at Stafford Hospital that resulted in hundreds of deaths.
The chair of the inquiry into Mid Staffordshire NHS made 290 recommendations to prevent the 'disaster' of Stafford Hospital occurring again.
Managers at Stafford Hospital accept that there were problems on some of the wards. But they say it's now one of the best in the country.