If the bill is adopted, the lyrics would change from "in all thy sons command" to "in all of us command".
The initiative is backed by the Liberal government and will reach the Senate soon, having passed two readings in the House of Commons.
The fight to change two words to O Canada has stirred a passionate debate.
Who wants to change the lyrics?
A similar idea to change the lyrics was rejected in 2010 by Conservatives, who held the majority in parliament.
Longtime liberal MP Mauril Belanger started the initiative this time with Bill C-210, and many in Parliament view the bill as his legacy project. Mr Belanger is sick with amyotrophic lateral sclerosis, or ALS, and uses a computer with a voice generator because he can no longer speak.
The Ottawa Citizen reports that there has been a push by Liberals and New Democrats to move the bill for Mr Belanger's sake, while some Conservatives want more time to debate the bill because of the anthem's significance to Canadians.
What's the case for a gender-neutral anthem?
In May, Mr Belanger presented the case for his bill: "On the eve of the 150th anniversary of our federation, it is important that one of our most recognised and appreciated national symbols reflect the progress made by our country in terms of gender equality."
"We are in 2016. The Canadian population will understand why we want to make the change," New Democrat MP Christine Moore said. "It is not a big change, and there will not be a big difference in the national anthem, but the difference is significant for women all across Canada."
Liberal MP Greg Fergus said it "would be nice if [Canada] stops excluding women from the national anthem", according to the Ottawa Citizen.
Why stick with tradition?
Some Conservative MPs have voted yes to the bill, but others want more time to debate the issue.
"It is tragic that this is being done in a fashion where Canadians are being shut out," Peter Van Loan, a Conservative MP, said in committee last week, the National Post reports. "Their national anthem is being changed. They have been singing it for decades, millions of Canadians. It belongs to them, it is not a plaything of us."
"We are telling Canadians, 'Guess what, you don't have a say in your national anthem. It belongs to us as politicians ... for us to deliver our worldview to you and impose it upon you'."
O Canada, originally composed with French lyrics, became the country's national anthem in 1980.
The first English version included the lines "Our home, our native land, True patriot love thou dost in us command". But during World War 1 that phrase was changed to "in all thy sons command" in an effort to stir patriotic feelings.
Other countries have changed their national anthem lyrics to make them more inclusive. In Austria, for example, a lyric about "sons" was changed to "sons and daughters" and a lyric about "fraternal choirs" was changed to "jubilant choirs".
In Switzerland, a contest was held to replace the country's national anthem in 2015, but the government has not decided on a winner yet.
The Canadian parliament is considering passing legislation that will make the English version of the national anthem gender-neutral.