According to the Mail on Sunday newspaper, Mr Adams is being sued for allegedly masterminding the 1996 Manchester and London Docklands bombings, alongside the 1973 Old Bailey car bombing attack.
The newspaper revealed that the 73-year-old was served notice of the High Court claim by lawyers of the victims last week.
Mr Adams has always denied any membership of the IRA and has refuted any involvement in their terror campaign during the decades of the Troubles. He has never been prosecuted for links with any of the group's activities.
A spokesperson for the former Sinn Fein leader told the Mail on Sunday he “rejects the claims made in the notice of legal action”.
“His solicitor will deal with it,” the spokesperson added.
According to the claimants for the action, they are accusing Mr Adams of being behind the IRA’s mainland bombing campaign.
The IRA’s 1996 bomb in London’s Docklands resulted in the deaths of two people, with many others injured by the device which had been left in a lorry on February 9.
Later that same year in Manchester the terror group detonated a 3,000lb truck bomb near Manchester’s Arndale Centre on June 15 causing widespread devastation and leaving more than 200 people injured.
Those bringing the claims are seeking a nominal damages fee of just £1 in the case, with the action being funded through CrowdJustice, an online fundraising platform specifically designed for legal action.
Law firm McCue Jury & Partners, who are representing the three claimants, successfully sued IRA man John Downey in 2019 over his role in the 1982 Hyde Park bombing which killed four soldiers in the Royal Household Cavalry.
Jon Ganesh, a security guard injured in the 1996 Docklands attack, told the Mail on Sunday: “We have to make a stand and get justice for the victims. Not just my friends who died at Canary Wharf, or the three of us, but all victims of the IRA’s despicable campaign.
“It’s not about any money, which is why we’re only claiming for £1 – it’s about the principle. It’s a historic moment. And Gerry Adams will have a chance to defend himself in court and answer the allegations.”
Another claimant in the case is Barry Laycock, a rail worker injured in the Manchester attack.
The third victim, John Clark, is a former police officer injured in in the Old Bailey bomb attack which killed a man and injured more than 200.
Matthew Jury, of McCue Jury & Partners, told the newspaper: “All the claimants are seeking is the truth, for them and on behalf of all the IRA’s victims.
“It’s an opportunity for Mr Adams to give his full and honest account of his part in The Troubles. If not, then it will be for the court to decide what role he played.”
Sinn Fein and Mr Adams have been contacted for a response.