A barrister representing three of the city's tree campaigners during their fight against injunction proceedings by Sheffield Council claimed on Thursday that Amey received the conviction in 2008.
John Cooper QC said the incident, when a pit collapsed killing a worker, was the first corporate manslaughter conviction.
He asked the council's head of highways Paul Billington whether or not he knew about the alleged conviction when the Streets Ahead road repair and maintenance PFI contract was signed in 2012 - to which Mr Billington replied he didn't.
Mr Cooper told the High Court in Leeds that the conviction meant the Streets Ahead contract was 'illegal'.
But yesterday Amey responded through its official Twitter account to refute Mr Cooper's claims.
A spokesman said: "Neither Amey or any company in the Amey Group has ever been convicted of corporate manslaughter.
"The references made to corporate manslaughter in the High Court are not recognised by Amey.
"We take the health and safety of our employees extremely seriously across all work that we carry out.
"As parts of the Streets Ahead contract we work closely with Sheffield Council to ensure our health and safety procedures are appropriate for the work being undertaken."
According to the Crown Prosecution Service the first corporate manslaughter conviction was for a company called Cotswald Geotechnical Holdings. The firm was found guilty in February 2011 in relation to the death of 27-year-old worker Alex Wright, who was killed when a trench on a plot in Stroud collapsed on top of him in September 2008.
The company is now dissolved, but appears not to be connected to Amey.
Amey Infrastructure Services was one of two companies fined Â£30,000 in December 2011 after electrician Peter Cole, 61, fell to his death from a cherry picker while fixing street lights in Merseyside.
The firm and Mouchel Parkman Services admitted failing to adhere to record checks designed to ensure the safety of the cherry-picker or mobile elevating work platform.
But this case was not discussed in court and it is not known whether or not the council was aware prior to the signing of the Streets Ahead contract.
Tree campaigner Richard Davies raised the case at a recent council meeting and was promised a written response.
Mr Justice Males is likely to give his ruling on the tree protest case in the High Court in London in two weeks.
The council is seeking permanent injunctions against Alison Teal, Dave Dillner and Calvin Payne, along with 'persons unknown'.
Campaigners object to the felling of healthy trees under the Streets Ahead contract, but the council says people are protesting inside safety barriers 'unlawfully' and as a result holding up work - which is costing the taxpayer money.
If the campaigners are served with injunctions and break them they will be in contempt of court, and could face fines or even prison.