The new allegations date back to between 2010 and 2012 when the two Conservative MPs were members of the Treasury Select Committee.
According to the newspapers, Mrs Leadsom made her complaint to Downing Street about Sir Michael on Monday, the same day she made a statement to Parliament confirming a Cabinet Office investigation into sexual harassment allegations in Westminster.
She told MPs in the House of Commons that staff who felt mistreated must be able to come forward in a “safe” environment and that MPs “must take action in days not weeks”.
A spokesman for Sir Michael confirmed on Tuesday that he was once rebuked by a journalist, Julia Hartley-Brewer, for putting his hand on her knee during a dinner in 2002, and he apologised at the time.
A day later, he resigned as defence secretary, telling the BBC: “We’ve all got to look back now at the past, there are always things you regret, you would have done differently.”
He was replaced on Thursday by Chief Whip Gavin Williamson.
Ms Hartley-Brewer said that if he had gone because of her knee, it would be “the most absurd reason for anyone to have lost their job in the history of the universe,”
After his announcement, the BBC’s political editor Laura Kuenssberg said that sources close to him did not believe he is “some kind of predator”, but that he had not felt that he could guarantee that he would be able to account for every encounter in his long ministerial career.