Cameron flies to Berlin Friday, where he will press his viewpoint with Chancellor Angela Merkel, the BBC said.
Cameron and Merkel also will discuss the Group of Eight summit in London, as well as Syria, his office said.
Cameron's Conservative Party has been reluctant to consider closer ties with the European Union but the prime minister wants to pursue key leaders to tell them he wants to remain in the bloc, provided it adopts reforms that would diminish its influence on the national powers of its members, The New York Times reported.
France and Germany both opposed Cameron's view when he announced in January he would hold what was called an "in-out" referendum on Britain's membership in the European Union if the Conservatives win national elections in 2015.
Cameron said this week the best outcome for Britain would be "membership of a reformed European Union."
In the interviews with five European newspapers, Cameron said the bloc had "sometimes overreached itself with directives and interventions and interference."
"I think we can have a flexible Europe where we don't all have to do the same things in the same way at the same time," he added.
He also emphasized it was vital to respond to failing support for the European Union in Britain, describing support for Britain's membership as "wafer thin."