Stephen Deans, the former Unite convener at the Ineos plant, resigned from his position last month before he was due to meet with management over claims he spent a significant amount of company time working on Labour business.
He was also implicated in the row over the selection of a Labour candidate to replace Eric Joyce in Falkirk – where Mr Deans is party chairman – and subsequent alleged attempts to thwart a party investigation.
However, the constituency Labour party in Falkirk West is expected to elect a new chairman tomorrow, when members hold their annual meeting.
Gray Allan, an official with the Unison union, said he was “prepared to accept nomination” if members wanted him to take over the post.
He said: “It’s a democratic matter for Labour Party members, but if my name is moved by people at Sunday’s meeting I’ll accept the nomination.”
It had been claimed that Unite packed the Falkirk constituency party with its supporters in an attempt to have its favoured candidate selected.
The allegations led to Mr Deans and Karie Murphy, Unite’s choice to replace Joyce, being suspended by Labour as it investigated the claims.
It is not clear whether Mr Deans, whose suspension from the party has been lifted, will attend the meeting at Camelon Labour club on Sunday.
Meanwhile, a selection panel made up of Labour officials will, on Tuesday, interview potential candidates to be the party’s candidate in the Falkirk West constituency at the next general election.
A final shortlist will then be drawn up which is likely to go before party members on 8 December.