Andrew Mitchell, 57, who was forced to resign from the Cabinet last year following the news reports, has repeatedly denied the claims. The Conservative party MP had insisted he had been a victim of a deliberate campaign to "toxify" his party and ruin his career.
Mitchell had admitted there was an ill-tempered exchange with officers after being told he could not ride his bicycle through the gates of Downing Street, but insists he did not use derogatory words attributed to him such as "plebs", which led the incident being branded as the "plebgate" affair in the British media.
"We stand by our story and will defend this claim vigorously," a spokesman for the tabloid said.
Murdoch's News International, owner of 'The Sun' and the now defunct 'News of the World', is already facing court action in a phone-hacking scandal and has given payouts to a number of public figures and celebrities in damages.
More From This Section
Scotland Yard is trying to establish how 'The Sun' and 'Daily Telegraph' obtained information about the "plebgate" row and if it came from police.
So far, three police officers have been arrested as part of the investigation sparked by the row on this incident which took place on September 19 last year.
Two policemen were on duty in Downing Street that day and are accused of leaking information to the media, while the third officer who was not working there at the time is suspected of misconduct. All three remain suspended. A 23-year-old man who does not work for the police was also arrested and bailed until May.