The Hollywood Reporter confirmed Monday the 50-year-old actress is poised to portray Thatcher in Season 4 of the Netflix series.
Sources said Anderson's deal has been in the works since April but has not officially closed. Season 4 will focus on Thatcher and Princess Diana, although it is unclear if Anderson would also appear in Season 3.
Deadline said Sunday that viewers will likely have to wait to see Anderson in Season 4, which is expected to take place in the 1970s. Thatcher served as British prime minister from 1979 to 1990.
The Sunday Times also reported Anderson will play Thatcher, nicknamed the "Iron Lady," in the fourth season.
The Crown, which follows the reign of Queen Elizabeth II, will feature new actors in Season 3 as the show's timeline progresses. Olivia Colman will replace Claire Foy as Elizabeth, with Tobias Menzies to assume the role of Prince Philip from Matt Smith.
Anderson is best known for playing Dana Scully on the Fox series The X-Files.