Lawyers for Mr Shepherd, who is also a former head of the Business Council of Australia and chaired Tony Abbott's Commission of Audit, wrote to Bacon last week demanding a correction to her tweet, which she sent on Friday, February 13.

The tweet, which was retweeted three times, referred to Mr Shepherd's role as chair of the consortium that won the Lane Cove Tunnel project.

Traffic forecasters working on the Lane Cove Tunnel, built between 2004 and 2007, massively overestimated the number of cars using the road.

Last year AMP Capital Investors, the manager of two funds that lost money when the tunnel opened, sued traffic forecasters Parsons Brinckerhoff and Booz Allen Hamilton over their work on the project.

During the legal battle, which was settled for an undisclosed amount, Mr Shepherd's role as chair of the consortium bidding for the project was also mentioned.

Mr Shepherd was a participant in meetings in which the requirement to increase traffic numbers was discussed.

The court heard Mr Shepherd was concerned that initial traffic projections for the project were too low. The businessman has since said his chairmanship of meetings was "facilitative" and he was not deeply involved in the construction of the bid.

Ms Bacon's tweet, which was part of a conversation about the lack of public information about the WestConnex motorway project, referred to Mr Shepherd's involvement in the Lane Cove Tunnel project.

Mr Shepherd's lawyer, Peter Keel of Ash Street, wrote to Bacon last week saying the tweet gave rise to imputations that were "false, clearly defamatory, indefensible, and manifestly of the utmost seriousness".

He requested Bacon make a correction in another tweet, and pay for a correction in the Sydney Morning Herald, The Age, and the Financial Review. If she did not, his client would reserve his rights to go to court.

Bacon said she would not be apologising and not be complying with Mr Shepherd's demands.

"I find it disappointing that Tony Shepherd would attempt to use the defamation laws to silence me," the journalist, who taught at the University of Technology Sydney and who is supporting the Greens at the coming state election, said in an email.

"Perhaps Shepherd would do better to reflect on the failure of the WestConnex Delivery Authority to properly consult with the community about a project that will worsen Sydney's transport crisis, both for residents in the western suburbs as well as the inner west."

Mr Shepherd told Fairfax Media that he was serious about the legal threat.

"You work hard all your life and the only thing that comes out of it is your reputation," Mr Shepherd said. And then "comes a cheap shot from somebody who doesn't have a clue".

"I am serious. I don't go to the trouble and the expense of engaging a lawyer for the fun of it."

The WestConnex Delivery Authority, which is responsible for building the 33 kilometres of planned motorway, will hold an information session on Monday night at Enmore Theatre.