The film ended with Bickle being hailed as a hero by the press, a perfect finale for a work that satirised the American loner and the cult of celebrity, said The Guardian.
De Niro was quoted by the New York Post as saying: "I was talking with Martin Scorsese about doing what I guess you'd call a sequel to 'Taxi Driver', where (Bickle) is older."
The original film charted the violent life of a Vietnam war veteran who becomes obsessed with the salvation of a child prostitute - played by Jodie Foster.
It is not known if Paul Schrader, who wrote the original film, will be involved in the sequel.