Reuters / Peter Nicholls
The Telegraph reported that the protest will start in Trafalgar Square and end in Parliament Square, within sight of the court where the judges will be hearing the case, which is due to start on December 5.
On Thursday last week, the government lost a High Court case which ruled that Prime Minister Theresa May must seek a vote in parliament before she can trigger Article 50, the formal legal mechanism a country must use to leave the European Union. She had previously argued that she could use the "royal prerogative," an ancient legal device, to trigger Britain's departure from the union.
The government appealed the High Court decision, taking it to the Supreme Court - the highest in the country.
The pro-Brexit group planning the march, Leave.EU, said it also plans to "crowd-fund" £100,000 from supporters to pay for barristers to bolster the government's legal representation in court.
Organisers at Leave.EU, which had the backing of Farage in the run-up to the June referendum, said that the UKIP leader had already "secured support from thousands of Leave voters" for the march and legal action.
The Supreme Court has set aside four days for the hearing, which will also be live-streamed on the internet.
A Leave.EU spokesman said the march would be "a reminder about what we voted for, so there is no slippage on the single market which we think this case was used to get a negotiating stand on."
He said: "We will also be launching, with all Leave campaigns including members of all political parties, a march on the Supreme Court to make a point that 'Brexit means Brexit'.
"This will remind the Government, politicians and the establishment, including the court, that they cannot ignore the democratic vote of the people in the referendum," he added.
The news came after Nigel Farage clashed on the BBC's Andrew Marr show with Gina Miller, the lead claimant in the Article 50 case, and warned of "disturbances in the street" if the result of the referendum was not respected.
Watch the full exchange below:
The referendum result must be respected. Leave means Leave: out of the single market. #Brexit pic.twitter.com/vXrbj6oAKj
- Nigel Farage (@Nigel_Farage) November 6, 2016