The "Fleabag" actor - who, at 44, is just a year older than the politician was when he was elected Prime Minister in 1997 - has reportedly had talks with Netflix bosses about starring in the fifth season of the show, which is expected to cover the death of Princess Diana in a car accident and the aftermath of the tragedy.
"This role is one of the most anticipated castings on 'The Crown'," a source told Britain's The Sun newspaper. "The final series covers the Prime Minister's epic clash with the Queen over her response to the death of Diana in 1997."
"So the creators wanted an adaptable actor like Andrew who has proved he can master the charm and intimidating presence that typified Blair."
However, Andrew's agent said he is "unavailable" for the current filming dates, but Dominic West had faced a similar hurdle until he reshuffled his schedule in order to take over as Prince Charles from Josh O'Connor.
According to Variety, production on the next series of the regal drama will begin in July (21).
The fifth season will see another cast refresh as the key figures enter new stages of their lives, with Imelda Staunton taking over as Queen Elizabeth from Olivia Colman and Tobias Menzies handing over Prince Philip to another former "Game of Thrones" star, Jonathan Pryce.
Lesley Manville will replace Helena Bonham Carter as Princess Margaret and "Tenet" actress Elizabeth Debicki will play Princess Diana in the latter part of her life, taking over the role from Emma Corrin.