But Mr Norris said the Duchess was still involved with the theatre.
He told the Daily Telegraph: "She is still very engaged, the conversations are regular and ongoing, there are ideas we are exploring.
"There has been no indication at all from her that her engagement with us would be anything other than business as usual – she has proven to be a very engaged patron, and we look forward to working with her."
Mr Norris added that Meghan had "star reach" and understood what the organisation was trying to achieve.
The theatre has become known in recent times for its community theatre programmes as much as for hosting performances from Ralph Fiennes and Cate Blanchett.
It will have achieved Mr Norris' five-year targets of 50 per cent of its writers, directors and actors being female as well as 20 per cent of writers and directors and 25 per cent of performers being "people of colour" by next year, the artistic director said.
Mr Norris also said he was looking forward to the Prime Minister Boris Johnson's forthcoming biography of William Shakespeare.