Sky News quoted its correspondent as saying there was an "extreme Islamist suicide plot against Downing Street (a reference to the UK Prime Minister's residence)".
Sky News reported on Tuesday, citing sources, that the police had foiled a plot to assassinate May. However, it does not appear they were able to obtain or build any explosives.
The police said there were now 500 counter-terrorism investigations involving 3,000 people and more than 20,000 other people have been investigated in the past.
The pair was arrested in London and Birmingham on November 28 by the Metropolitan Police Counter Terrorism Command.
The UK terror threat from Islamist terrorists is operating "at a scale and pace we've not seen before", said Andrew Parker, director general of MI5, in a speech in October.
He appeared alongside 21-year-old Mohammed Aqib Imran, who was accused of trying to join the Islamic State (IS) and preparing acts of terror.
The PM's official spokesman declined to discuss the details of the attacks, but several newspapers later reported that the two men arrested in London and Birmingham last week had been behind the plot.
Both men, who indicated that they would plead not guilty, were remanded in custody until their next court appearance on December 20. According to the Independent, Rahman and Imran on Wednesday to be tried before the court in Westminster.
After the meeting, the Prime Minister's spokesman said: "The Prime Minister led thanks to the tireless work of staff at MI5 to combat the unprecedented terrorist threat". The then prime minister, John Major, was inside but was not hurt. Nobody was injured during that attack.