Hanks is in talks to play Washington Post editor Ben Bradlee, while Streep would play the newspaper's publisher Katherine Graham, according to Deadline, although details are still being negotiated.
This year's Academy Awards was dominated by celebrities trying to repudiate Trump on and off stage. So a politically-charged movie that speaks to the times, headed by three of the greatest movie talents of our generation, is a project that would surely generate plenty of Oscar buzz next year.
Accepting the Cecil B Demille Lifetime Achievement Award, the screen legend made a passionate speech, attacking Donald Trump.
Streep recently defended the freedom of the press in a speech opposing US President Donald Trump at the Golden Globe Awards.
She encouraged people to donate to the Committee To Protect Journalists and criticised Mr Trump's impression of a disabled reporter, saying it "kind of broke my heart".
The Post would mark Spielberg and Hanks' fifth film together after Saving Private Ryan, Catch Me If You Can, The Terminal and Bridge Of Spies.