Two men were allegedly plotting to use a bomb disguised as a bag to blow off the gates of Downing Street and then attack May with knives, The Independent reported.
Naa'imur Zakariyah Rahman, 20, from north London, and Mohammed Aqib Imran, 21, from Birmingham, have been charged with preparing a terrorist act. They are due in court on Wednesday.
MI5 head Andrew Parker revealed information about the plot to the British cabinet, The Independent and Sky News reported.
A Scotland Yard spokesperson declined to confirm to The Independent whether the arrests were linked to a plot to attack the prime minister.
May and other British leaders were sharply critical of President Trump last week after he retweeted a series of videos on social media purporting to show violence committed by Muslims. Jayda Fransen, the deputy leader of the far-right group Britain First, first posted the videos.
"The fact that we work together does not mean that we're afraid to say when we think the United States has got it wrong, and to be very clear with them. And I'm very clear that retweeting from Britain First was the wrong thing to do," May said.