Nicky Morgan has aimed a swipe at fellow potential Conservative leadership candidates by saying the contest must not be fought between two "white men".

The education secretary, who is a Christian, spoke to the Birmingham Mail and suggested that she may stand for Conservative leadership when David Cameron resigns, which he has said will happen before 2020.

"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."

Under Conservative Party rules, Tory MPs nominate two candidates and the final vote is then down to party members. Assuming Cameron resigns before 2020, as he has indicated he will, the winning candidate would automatically become Prime Minister and lead the party into the next general election.

Morgan's comments are likely to raise tensions in the Cabinet as rival candidates begin their subtle campaign to win nominations from fellow MPs. The jibe was most probably aimed at George Osborne and Boris Johnson, the two leading candidates.

As well as drawing attention to her own credentials, the comments will also be a boost for other trailing candidates such as Theresa May, Sajid Javid and Priti Patel.

Last October Morgan was the first Cabinet member to publicly state she was considering running for leadership. She said she may enter the race but "a lot of it will depend on family".