The Independent on Sunday reported that detectives were said to be investigating an allegation that Brittan, who was not an MP at the time of the alleged incident, assaulted a woman at an address in London in 1967. Brittan was in his late 20s at the time of the alleged incident.
The Metropolitan police said: "A man aged in his seventies was interviewed under caution by appointment at a central London location in connection with the allegation. He was not arrested."
The Independent said he refused to comment on the claim. It quoted him saying: "I'm sorry I am not going to be able to talk about something like that."
In a statement, Scotland Yard said in late 2012 a woman claimed to police that she was raped by a man at an address in London.
The BBC also reported that it understands that man interviewed was Lord Brittan, who was home secretary in Margaret Thatcher's Conservative government from 1983 to 1985.
Brittan, who was first elected as an MP in 1974, later became Trade and Industry Secretary. He stood down from the Commons when he became a European commissioner in 1989.
