The Energy Minister said she had a “wide range of support” but that it was too early to talk about jobs or roles for the UKIP leader.
Leadsom was also forced onto the defensive after it emerged that she had forecast just three years ago that the UK quitting the EU would lead to economic “disaster”.
The former City financier, tipped as the favoured choice of most Eurosceptic Conservative MPs amid a backlash against Michael Gove’s ‘treachery’, said she had been “on a journey” since her remarks in 2013.
With Leadsom rapidly emerging as the main challenger to Theresa May, she was on asked on BBC1’s Andrew Marr Show if she would consider Farage as part of her negotiating team in detailed talks with the EU on how Brexit would happen.
“I don’t want to get into who would do what,” Leadsom replied. “What we need is somebody to lead the campaign who really believes in the opportunities.”
Leadsom was also asked why she was attracting backing from UKIP supporters.
Arron Banks, the millionaire ally of Farage, said this weekend that Leadsom was “the breakout star of the Leave campaign during the referendum” and that his leave.eu organisation would be “throwing its full weight behind Andrea, particularly online”.
Leadsom told Marr: “Arron Banks is one person, that’s true. I don’t think it’s fair to say I’m just being supported by UKIP.
“I’m delighted by the wide range of support, particularly from young people.”
Some on Twitter were surprised that Leadsom hadn't ruled out a Farage post, while others felt she simply answered a straight question with a candid answer that didn't commit her to anything.
Historian Simon Schama felt it was a mistake not to make clear that the UKIP leader would have no role.
But others felt it made sense to unify the Leave camp in the national interest.
Leadsom's remarks came as a new Sun/ICM poll put May way out in the lead of the Tory leadership battle, attracting 60% support from Tory members, compared to 10% for Gove and 6% for Leadsom.
Leadsom said that the country needed to be lead by a figure who genuinely believed in Brexit, to implement the result of the EU referendum.
In a dig at May, she said: "Somebody who says 'OK, I've been told to leave, so I'll leave', with no enthusiasm is very different to somebody who absolutely sees the sunlit uplands of leaving the EU, the prospects for our children, our grandchildren, our business, of being open to the world."
Leadsom, Gove and May all agreed to publish their tax returns as part of the leadership race.
Tory grandee Lord Tebbit, who attacked May for overseeing a huge rise in immigration, also said Leadsom was the only “credible” candidate in the race.
Leadsom was accused of being a 'hypocrite' after the Mail on Sunday revealed remarks from a speech in 2013 in which she said: “I don’t think the UK should leave the EU.
“I think it would be a disaster for our economy. And it would lead to a decade of economic and political uncertainty.”
Today, she said that she would trigger Article 50, the legal instrument needed to start Britain's formal exit from the EU, as soon as she won the Tory leadership in September.
Gove said on Friday he would trigger it by the end of the year, whereas May said again today she would wait until 2017.
When confronted with her words from three years ago, Leadsom told Marr: “It has been a journey… That speech was April 2013 and things have so moved on.”
She said that during her travels across Europe with her ‘Fresh Start Project’ she realised how difficult it would be to get “fundamental reform” of the EU.
“I had been very clear in the rest of that speech…the status quo was not an option.
“When the Prime Minister came back with his reform, with his negotiation [in February], it was very clear that the EU was just not reformable.”
Leadsom said that since 2013, “the risks of remaining in the EU massively magnified”, with soaring youth unemployment in the Eurozone and a “massive migration crisis”.
Gove was repeatedly quizzed on the Marr Show about his decision to withdraw his support for Boris Johnson and instead go for the leadership himself.
The Justice Secretary said that "if you put friendship and personal relationships before what is right", the national interest would not be served.
Gove said that "I talked to my closest colleagues and my wife [the Daily Mail columnist Sarah Vine]...and I then made that decision."