The FT said May told Defence Secretary Gavin Williamson that he needed to rethink the capabilities needed to be a modern military force and focus more on Britain's ability to tackle any cyber warfare threats, including from Russia.
May's intervention created shockwaves at the defence ministry, the FT reported, without citing a source.
May's office acknowledged that Secretary Williamson's plans had been challenged by May at a meeting on Tuesday but dismissed suggestions that she was arguing for a reduction in Britain's military status, the FT said.
"The prime minister is strongly committed to the United Kingdom's armed forces and to maintaining their strength and their ability to deter and where necessary defeat the threats we face."
A spokeswoman for Downing Street did not immediately comment when contacted by Reuters. The Defence Ministry was not immediately available for comment.