The Most Rev Justin Welby said he believes a woman will one day be made archbishop and added that some gay couples have loving relationships of "stunning quality", ahead of today's enthronement.
Pressed on the timing, he said: "Oh, I have no idea...when the right person turns up. But, yes, I think there certainly will."
In a separate interview with BBC News, the Most Rev Welby backed traditional Church teaching on homosexuality but said: "You see gay relationships that are just stunning in the quality of the relationship."
More top news
A woman who attempted to get her idol's full pout was left with hugely swollen lips when her plan went horribly wrong.
All would-be MPs should be forced to tell voters what paid jobs they have and whether they would keep them if elected, Lord Bew has said.
A Para who won the Victoria Cross gave up his military history studies just weeks into the course as he wanted to be a part of it instead.