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.
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Rebecca Johnson, 25, was working as a tour guide with the Santa Safari team when she was killed.
Bahrain couldn't be more different to the UK right now.
Mrs May denied she was forced to "grub around" for deals as she said that the UK will raise human rights with Gulf leaders at summit.