Thailand has hosted the annual military exercise with the US and many Asian countries since 1982.
But Washington said it would consider relocating it to another country after the Thai military launched a coup to topple the civilian government on May 22.
As long as no decision has been made, the status of Cobra Gold is still under consideration, a US Embassy source said.
A senior military officer told The Nation that the US had asked Thailand to join Cobra Gold as usual next year.
The junta then asked the US to explain in writing why they wanted to have the joint drill with Thailand after they had threatened to exclude its treaty partner, the source said.
The US Embassy has made no official comment on the report but an official said there was normal communications between the military of both sides while the policy is still intact.
Scot Marciel, deputy assistant secretary of state, said last month that the Obama administration was required by law to review military cooperation with Thailand after the coup.
Washington has suspended more than US$4.7 million of security-related assistance. High-level engagements, exercises and some training programmes with the military and police were cancelled.
The CARAT (Cooperation Afloat Readiness and Training) bilateral naval exercise and Hanuman Guardian army exercise were also suspended.
The US had also cancelled Thailand’s invitation to a maritime warfare practice in Hawaii in June.