'When asked if Rishi Sunak's view, expressed at the Conservative Party conference, "a man is a man and woman is a woman" should be expressed on campus, he said: "As long as a view can be legally expressed, such as that one, then yes, but so is the opposite."
Prof Ahmed added: "There is no question whatever that we have any interest in the culture wars - we don't - or that we have any interest in defending any one political side - we absolutely don't.
"On both sides of any issue, we will be equally vigorous in defending the free speech rights of students, academics and visiting speakers."
He also cited the UK's falling rank on the Academic Freedom Index, which has collected data on freedom of expression since 1900.
A new law, passed earlier this year, says universities now have a duty to "secure" and "promote the importance of" freedom of speech and academic expression. Higher education providers and student unions which fail to comply may face sanctions, including fines.
Prof Ahmed will also oversee a new complaints scheme for students, staff and visiting speakers, who could seek compensation if they suffer from a breach of a university's free speech obligations.
That complaints process will come into force next August, and is currently under consultation.
In his speech at Kings College London on Monday, Prof Ahmed is expected to say he will protect people who want to express their views on "Brexit... on statues, or pronouns, or colonialism, or abortion or animal rights, or Ulez".
Some speech, such as that which amounts to harassment or incites violence, is not protected by the law or by freedom of speech.
"You can speak or write as a Marxist, a post-colonial theorist, a gender-critical feminist or anything else - if you do it within the law," Prof Ahmed is expected to say.'