Baroness Hale, who was born in Leeds and lives in Richmond, North Yorkshire, suggested she would raise the idea with other judges and staff at the court.
Lady Hale, the first woman to hold the job, told The Yorkshire Post it was important to ensure the judiciary “looks familiar” and feels like “part of us” as a country, “rather than some group from another planet".
She called for “affirmative action” to get more women, state educated and ethnic minority people into the profession.
And she recognised the value of having major institutions move outside London, even if only temporarily.
The Supreme Court sat in Edinburgh last year, and is due to sit in Belfast this year and Cardiff in 2019.
Lady Hale said there is “quite a logistical problem” in transporting judges and broadcasting equipment to different parts of the country.
But she made clear in Saturday’s newspaper: “I would dearly love us to sit in the North of England.
“We have a lot of cases that come from the North of England so if we were to sit somewhere central in the North of England I would love to do that.
“But I doubt it will be practical when I’m around.
“I might start raising the idea.”
Read the full interview in The Yorkshire Post on Saturday.