The Archbishop of Canterbury added in the interview that a proposed new role would be for a "presidential figure who can travel more readily".
The 62-year-old is to step down in December after 10 years as Archbishop of Canterbury to take up a new post as Master of Magdalene College in Cambridge.
More top news
President Trump's administration have reinstated a likeness of Winston Churchill to the White House's most famous room.
Data-selling companies trade personal addresses and phone numbers for as little as 4p per record, a watchdog has warned.
A bitterly cold airmass covers the UK this weekend.