According to a senior Labour source Stevie Deans's post will be up for re-election at the local party's annual general meeting in three weeks' time.
It comes amid growing calls for leader Ed Miliband to re-open the party's investigation into alleged vote rigging.
Mr Miliband has refused to reveal details of what the party's investigators found following accusations that Unite attempted to fix the race to be Labour's Falkirk candidate at the next election.
But he is under increasing pressure to do so after leaked emails appeared to show the original inquiry had found "forgery, coercion, trickery and manipulation."
Senior Tory MP Priti Patel has demanded Mr Miliband re-open the case, while local members in Falkirk have called on him to publish the results of the original inquiry, carried out earlier this year.
Scottish Labour last night called for the party to move on from the accusations, which have dogged it for months.
A spokesman said it was now "focused on ensuring we have a fair and transparent selection and that the local party has a new candidate they can get behind for the 2015 General Election."
But local party sources in Falkirk expressed their dissatisfaction with that stance.
One said: "It is just not satisfactory to try to ignore this as if it never happened.
"But that is exactly what they are trying to do."
In his role as chair, Mr Deans signed up dozens of new members to the local Labour party.
But he found himself at the centre of allegations that Unite was trying to pack the party to ensure its favoured candidate, Karie Murphy, was selected.
Prime Minister David Cameron has also accused Mr Deans of being a rogue operator who almost single-handedly lost 800 jobs at Grangemouth.
The official has resigned from his job at Grangemouth after a separate investigation by the plant's owners Ineos into allegations he was carrying out Labour Party business while at work. This includes claims he attempted to secure the Falkirk selection.
In a separate move a would-be candidate for the Falkirk selection was also reported to have accused former Labour election chief Tom Watson of being "involved in it all behind the scenes".
There had been speculation that Mr Deans might be ousted at a meeting of the local Labour party yesterday, but his position was not discussed.