Quoting a top lawyer reviewing the case for the Crown Prosecution Service, The Sun tabloid said there appeared to be insufficient evidence of criminal offences in the killing of Jean Charles de Menezes on July 22 last year.
As a result, no charges will be made against the officers who shot the electrician or the senior figures in charge of the operation, the daily said.
Its source, identified as "an authoritative legal" figure, told the newspaper: "Mistakes were made but they do not amount to criminal misconduct.
"The firearms officers were acting under orders. Those in charge of surveillance believed he was a suspect.
"There is no realistic prospect that they will be prosecuted."
The Sun noted, however, that such an outcome may put more pressure on Sir Ian Blair, the Metropolitan Police chief, to take responsibility for the fatal error.
Blair has faced calls to resign from friends and relatives of De Menezes.
The Brazilian was killed on a train in Stockwell Underground station in London a day after a failed attempt to mimic the July 7 suicide bombings in the British capital which left 56 people dead.
The 27-year-old was shot by mistake under a controversial shoot-to-kill policy for suspected suicide bombers. Police shot him eight times.