The Prime Minister ordered a series of reports on the influence of the EU earlier this year, as the first step towards negotiating a new relationship with Brussels, reports The Daily Telegraph.
The focus is on Britain's own situation but the Government also sent a survey to all 26 member countries asking for their opinions on the balance of power between the EU and national parliaments.
However, Mr Cameron's two powerful allies, Germany's Angela Merkel and France's Francois Hollande, have declined to take part in the exercise.
According to the Financial Times, the French see the review as a product of British domestic politics.
Countries including Italy and Sweden are thought to have taken part, but not the majority of nations.
The lack of responses signals that Mr Cameron may have trouble winning support among EU leaders for repatriating powers to national parliaments.
Read more of this report from The Daily Telegraph.