Mr Carney, who started his role on Monday, said he is discussing with colleagues how best to "celebrate the diversity of great British historical figures" and plans to make an announcement before the end of the month.
His comments follow a row over the choice of Sir Winston Churchill to appear on £5 notes in place of prison reformer Elizabeth Fry - one of only two women selected since historical figures were introduced in 1970. The decision to use the wartime leader in April led to an online petition and the threat of potential legal action under the Equality Act.
Mr Carney's predecessor Sir Mervyn King recently revealed that Pride and Prejudice novelist Jane Austen is the leading candidate to replace Charles Darwin on the £10 note, as and when the notes are changed.
Conservative MP Mary Macloed wrote to Mr Carney earlier this week on the subject, complaining that "on the very notes that we earn and spend, we will now see no women at all".
In his response, Mr Carney said he considers Sir Winston to be an "excellent choice" for a banknote, but the Canadian said he recognised that in the absence of any other changes to banknotes, "none of the four characters on our notes would be a woman".
Mr Carney said "that is not the Bank's intention" and continued: "I believe that our notes should celebrate the diversity of great British historical figures and their contributions in a wide range of fields."
Mr Carney said he has already begun discussions with colleagues on how best to ensure notes represent a diverse range of people.
He said: "These will include a discussion at the next meeting of the Court of the Bank on 17 July. I expect to make a public announcement once those deliberations have been completed and no later than the end of July."