The Business Secretary revealed the controversial strategy ahead of make-or-break talks between the Prime Minister and Taoiseach Leo Varadkar in the north-west of England.
Under the terms of the Benn Act passed by MPs last month, Mr Johnson must send a letter asking for a three-month Brexit delay if no deal is done by 19 October.
Boris Johnson reassures moderate Tories he will not fight the election on a no-deal manifesto
Blow for Boris Johnson as Michel Barnier says EU ‘cannot accept’ UK Brexit proposals
Judges delay ruling on a bid to make Boris Johnson ask Brussels for Brexit extension
Number 10 has repeatedly insisted that while it will obey the law, the UK will leave the EU on Hallowe’en as planned.
Speaking to ITV’s Peston programme on Wednesday, Ms Leadsom explained how the Government planned to abide by that pledge.
“Well it’s quite clear that the Government’s policy is that we do not want a delay,” she said. “I don’t think anybody can be in any doubt about that.
“So I think it’s perfectly reasonable to make that point very clearly.”
Asked if that meant the PM would send a second letter disavowing the first one, Ms Leadsom said: “Absolutely.”
Elsewhere in the interview, the Cabinet minister also rejected suggestions that the UK could agree to a time-limit on the Irish backstop as a way of getting a deal across the line.
She said: “The UK will leave the customs union and the single market entirely whole, and there won’t be a backstop.”
Downing Street said Mr Johnson’s meeting with the Taoiseach was to allow “detailed discussions” to take place after Dublin reacted poorly to the PM’s Brexit offer last week.
Mr Varadkar said on Wednesday: “Part of the difficulty at the moment though is it is the position of the UK government that Northern Ireland must leave the EU customs union and be part of the UK customs union, no matter what the people of Northern Ireland think.
“That’s their position at the moment, and that’s the one that’s of grave difficulty to us.”
Elsewhere David Sassoli, the president of the European Parliament, said Britain will only be granted a Brexit extension if it agrees to hold a general election or a second referendum.
He set out the plans during a debate in Brussels after discussions with John Bercow, the Commons Speaker earlier this week.
It was backed by France’s Europe Minister Amélie de Montchalin, who said: “If there are new elections or a new referendum, if there is a political shift leading us to believe we could have a different dialogue from the one we have today, then an extension can be discussed.”
And Mr Johnson was branded a “real traitor” by Guy Verhofstadt, the European parliament’s Brexit negotiator, who accused him of seeking scapegoats for a no-deal Brexit.
He said: “The only one who is not to be blamed is Mr Johnson apparently.
“All those who are not playing his game are traitors, are collaborators, are surrenders.
“The real traitor is he or she who risks bringing disaster on his country, its economy and its citizens by pushing Britain out of the EU.
“That, in my opinion, is a traitor.”