The leader of the Commons confirmed that she was weighing up another leadership bid, having reached the final round of the 2016 contest before withdrawing from the race.
Ms Leadsom, a vocal Brexiteer, has strongly defended the prime minister's Brexit deal but admitted she was "disgusted" that the UK has still not left the EU almost three years after the Leave vote.
She suggested "things might have been different" had there been a "determined Brexiteer" in Downing Street, but defended Ms May's handling of Brexit.
The prime minister is facing fresh pressure to resign after the Tories' abysmal performance in local elections earlier this month. Her future is likely to be the main topic of discussion when Tory MPs hold their regular meeting on Wednesday afternoon.
Critics of the prime minister have urged the executive of the 1922 Committee, which represents backbench Tory MPs, to change party rules to allow another vote of no confidence in her this summer, but it has so far refused to do so. That could change if Ms May refuses to lay out a timetable for her departure.
Asked whether she was planning a bid to succeed Ms May, Ms Leadsom told ITV's Good Morning Britain: "I've supported her for the last three years to get Brexit over the line.
"She has said she is going, so yes I am seriously considering standing."
She added: "If you had a determined Brexiteer I suspect things might have been different, we might have been out by now on WTO terms, but on the other hand you would have left the country very divided."
Ms Leadsom insisted she was "sticking with the prime minister" to deliver Brexit, despite Ms May's failure to secure parliament's backing for her exit plan, and blamed MPs for the current deadlock.
Ms Leadsom said: “I'm absolutely making no apologies for parliament. I'm disgusted at the fact that nearly three years on we still haven't left the EU. We should have been out by 29 March."
She defended Ms May's deal but said she would be happy with a no-deal outcome, because Britain is "very well prepared".
Of the deal, she said: “I would say it's tolerable, it is leaving the European Union. It's not what I wanted - I've really struggled with it.
“I've always felt that no deal would not be ideal for the country [but] right now I would be prepared to have no deal. I think the country is very well prepared for that.”
The Commons leader also dismissed Nigel Farage's new Brexit Party as "a one trick pony" when asked about its surge in the polls.
She said: "They are about leaving the EU and actually they would find if they were in government, which they wouldn't be, they could not deliver this with this parliamentary arithmetic any more than the current government can."
But when it was suggested by presenter Piers Morgan that the new party could take enough votes from the Conservatives to keep the Tories out of power, she replied: "That is very true."
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