However, a spokesperson for the streaming service told DigitalSpy that the reports were "pure speculation".
"We are now filming Season 4 of The Crown but have not commissioned any further seasons as yet, therefore any news on casting remains pure speculation", a Netflix spokesperson said in a statement, per Variety.
From cold-war paranoia, through to the jet-set and the space age - the exuberance of the 1960s and the long hangover of the 1970s - Elizabeth and the Royals must adapt to a new, more liberated, but also more turbulent world.
The new season covers the epoch of 1964 to 1977. It originally starred Foy in the lead role, with Matt Smith as the Duke of Edinburgh and Vanessa Kirby as Princess Margaret. Also starring in season 3 were Josh O'Connor as Prince Charles, Erin Doherty as Princess Anne, Ben Daniels as Lord Snowdon, Jason Watkins as Prime Minister Harold Wilson, and "Game of Thrones" alumnus Charles Dance as Lord Mountbatten.
She was nominated for an Oscar for the title role in Mike Leigh drama Vera Drake, but is best known to many for playing the villainous Dolores Umbridge in the Harry Potter franchise.