"The PM has been clear in her support for the governor, the work he is doing for the country. It is clearly a decision for him, but the PM would certainly be supportive of him going on beyond his five years," the spokeswoman said, as quoted by The Guardian.
Carney, who became governor in June 2013, committed to serving for five years. However, he has since stated he is considering extending his contract to a full eight-year term that governors usually serve.
Earlier this month, May criticized the Bank of England for its low interest rates, to which Carney responded by saying that the Bank would not be instructed by politicians on how to model its policies.
Last week, Carney said his decision whether to stay would be based on personal rather than political considerations.
Carney is due to meet the prime minister later on Monday, and will hold a quarterly Bank of England news conference on Thursday.