In a column for the Daily Telegraph, Cameron wrote the government has bucked the trend of immigrants taking the majority of new roles, with domestic jobseekers filling the majority of positions created within the past 12 months.
"Progress is being made: while most new jobs used to go to foreign workers, in the past year more than three-quarters have gone to British workers," he said.
But UK Statistics Authority chair Andrew Dilnot revealed there are no official figures on the number of "new jobs" being taken by particular demographics.
"The official statistics provide estimates of net change in the number of people in employment. This is not the same as the number of people who move into employment," he said.
"From the available official statistics, it is, therefore, not possible to estimate the number of new jobs, nor the number of new jobs that are filled by UK nationals, nor the number of new jobs that are filled by non-UK nationals."
It is the second claim in Cameron's 28 July column to be questioned. Recruitment and Employment Confederation chief executive Kevin Green told HR magazine the Prime Minister's comments on recruitment companies looking abroad for talent were both "unfair and unhelpful".
