In a letter to EU foreign relations chief Catherine Ashton, the five countries asked her to investigate their options in moving forward despite objections from Britain, the online newspaper said.
The letter, viewed by EUobserver personnel, said Ashton should examine "permanent structured cooperation," a treaty option that allows nine or more member states to move ahead on projects without other EU countries.
Supporters of a military headquarters say the EU needs to move beyond battlegroups toward an EU army but Britain is highly opposed to the idea.
"I have made very clear that the United Kingdom will not agree to a permanent operational HQ. We will not agree to it now and we will not agree to it in the future. That is a red line," British Foreign Minister William Hague said in July.