Reuters
The Times newspaper ran a piece on Friday where it quoted Leadsome as saying May must be "really sad" about not being able to have children.
Leadsome is also reported to have said that having children means she has "a very real stake" in Britain's future.
The mother of three tweeted that she was "disgusted" with the interview, adding that it's "the exact opposite" of what she said.
Rachel Sylvester, The Times journalist that wrote the piece has said she was "baffled" by Leadsom's reaction.
Leadsome and May are the two women in the running to be the next Conservative party leader and therefore the next Prime Minister.
Firm favourite May is currently the Home Secretary while Leadsome is the MP or South Northamptonshire.
Truly appalling and the exact opposite of what I said. I am disgusted. https://t.co/DPFzjNmKie
- Andrea Leadsom MP (@andrealeadsom) July 8, 2016