Under Conservative Party rules, MPs pick two candidates who then take part in a ballot of Conservative Party members. The winner would become Prime Minister, and then lead the party into the next general election.
Highlighting comments made by the Prime Minister about the need to ensure black and ethnic minority students had a chance of going to university, she said the same could apply to the Conservative party.
She told the Birmingham Mail: “It’s very interesting this weekend that the Prime Minister was talking about diversity in university applications, and saying that our top institutions - not just universities - need to have diversity at the top.
“What I would probably say is I think it would be a big mistake if, when we get to it, the two people that the party offers up as potential candidates are white men.
“I have said before that I think it would be great to have a woman there.
“That might be me, it might be somebody else. But I think there are other great candidates.
“And we ourselves have to practice what we preach, which is having diversity at the top.”
It came as it was claimed that Mr Cameron has told allies that he will stand down in the spring of 2019.
Mrs Morgan said that she was contemplating standing as leader but that “a lot of it will depend on family”.
Mrs Morgan also backed a Darlington headteacher who asked parents to stop wearing pyjamas when bringing their children to school.
She said: “I fully appreciate that actually getting out of the house, co-ordinating choldren and all the rest of it - it can be really tricky in the morning.
“But I do also think that actually, it’s not that difficult to get dressed in the morning. It sets a standard really.
“So yes I back the head. I don’t really think pyjamas are suitable attire for going to school.
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