Amber Rudd said she is "keeping the door slightly ajar" to a possible run to be prime minister as she played down suggestions she would team up with Boris Johnson on a joint ticket to replace Theresa May.
The Work and Pensions Secretary said she "didn't have a plan" to stand in a leadership contest but repeatedly refused to rule out joining the race to be the next Conservative leader.
Speaking on Radio 5 Live's The Emma Barnett Show she was asked if she wanted to take over from Mrs May, who signalled she will stand down once Brexit is delivered.
Ms Rudd said: "I'm going to continue to support the Prime Minister, she has said that she is going to leave after the Withdrawal Agreement of the first stage is through so frankly what I think we should all be doing is trying to support her to make sure we do just that."
She added: "I can tell you I don't have a plan for it, I'm choosing my words carefully here."
Pressed on the issue the minister said she did not have a leadership strategy worked out, and asked if she was "working on it" she replied: "No, I'm not particularly working on it, I'm speaking to you very genuinely here, I'm just working on supporting the Prime Minister and getting this deal through, that's what's most important."
Ms Rudd added: "What I've said is that I'm not planning to run, so I have kept the door slightly ajar, but I'm not committed to it at the moment."
Asked about rumours she is planning on standing on a joint ticket with former foreign secretary Mr Johnson, nicknamed Bamber, Boris and Amber, by the press, she said she was "not supporting anybody".
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And she called his comments about Muslim women who wear a full face covering "completely inappropriate".
Asked if this would disqualify him from being a potential running mate she said "the area we really disagree on is how we leave the European Union", saying the One Nation caucus of Conservative MPs she started with ex-education secretary Nicky Morgan would not back a candidate who advocates a no-deal Brexit.
Presenter Ms Barnett said if the group fail to find someone who fits their criteria: "You're just going to have to step in aren't you?"
Ms Rudd replied: "That is entirely possible ... I don't rule it out."