Variety said Tuesday the film's producers are talking to Boyle, but have not made him a formal offer.
MGM declined to comment for the entertainment industry trade newspaper's report.
Daniel Craig is to return as the globe-trotting spy in the film, which is due in theaters Nov. 8, 2019, CinemaBlend noted. Craig previously appeared in the Bond films Casino Royale, Quantum of Solace, Skyfall and Spectre.
Sam Mendes directed the most recent 007 blockbusters Skyfall and Spectre, but has said he doesn't intend to helm another.