Banksman John Cousins was killed last year in the only fatal accident during the building of the giant structure.
So far, 1,566 people - many of them bridge workers past and present - have signed a petition to have a memorial placed on the bridge on its opening day.
Today (Fri), Transport Scotland confirmed that discussions are underway with the family of the 62-year-old from the Northumberland area about a memorial at the bridge.
A Transport Scotland spokesman said: “We understand that FCBC [Forth Crossing Bridge Constructors] has been in discussion with John Cousin’s family for some time regarding both a suitable memorial and whether they will attend any of the opening events.
“Obviously this is a deeply sensitive matter for them and we would like to respect their wishes for privacy at this time.”
The Change.org petition, set up by local campaigner Martin Keatings, calls for the memorial to also include a worker who died of natural causes during construction.
The petition to the Scottish Parliament states: “I believe it would be more fitting for the families of those men to at least be offered a participatory role in the opening of the new bridge.
“If not, at the very least, an honour should be erected on, near or included on the plaque about the bridge to immortalise them and recognise the fact that because they went into the line of work they did, people on both side of the bridge are able to use it because they contributed to its construction from the water up.
“I believe most would agree that it would be a fitting tribute to their lives and show that the legacy of their lives work in that industry has yielded a construction marvel of epic proportions which will enrich the lives of millions over the life of the bridge.”
Mr Keatings added that 57 workers died during construction of the Forth Bridge and it took 125 for them to be “publicly immortalised by commemoration on that bridge”.
Hundreds of heartfelt messages have been left on the page backing the petition.
Debbie Rowan from Glasgow wrote: “I work for the sole scaffolding contractor on the crossing and our men were nearby when one of these men lost their life.
“To say they were traumatised is putting it mildly.
“I think that for the memory of the people who gave their life for the construction of this landmark crossing and their families the least anyone can do is keeps their memory alive by doing something like this.”
James McAspurn from Glenrothes, Fife said: “I work on the bridge. Both the men should be remembered. John was a true gentleman and a friend.”
Andrew Edwards from Linlithgow wrote: “I worked alongside John Cousins. It would be nice way to remember him every time you cross the bridge.”
And Kirsty Keane from Linlithgow said: “Give these men the respect they deserve and for them not to be forgotten love and respect to their family and loved ones.”
Mr Cousins died when he was hit by the boom of a crane.
In a tragic irony, he had taken part in a minute’s silence to remember tragedies involving fellow construction workers across the world.
A second man was involved in the accident and was also rushed to hospital but his his injuries were not life-threatening.
On 6 February this year emergency services were called to the bridge after a 57-year-old fell ill.
He was taken to Victoria Hospital in Kirkcaldy, Fife but later died of natural causes.
More than 10,000 workers have been involved at various stages of the construction process with many being paid off as the the completion date looms closer.
The bridge will be officially opened by the Queen on September 4 with access to traffic starting two days later.