The contest to become the next leader of the Unite union is set for another twist after three leftwing rivals for the position failed to agree upon a unity candidate. Sharon Graham, the only female candidate, has told friends she will put her name forward for the final ballot despite two days of talks with fellow leftwing candidates Steve Turner and Howard Beckett. Beckett raised eyebrows in the negotiations after suggesting the impasse could be overcome by writing the names of each candidate on a piece of paper and drawing a single name from a hat. His suggestion was rejected. The development raises the prospect that all three left candidates will stand, splitting the faction’s vote and allowing Gerard Coyne, a Labour party member of 30 years who is generally supportive of Keir Starmer, to win. A well-placed source in the Graham camp said she had already decided to put her name forward for the final ballot and has “had it” with discussions. “She is finished with these negotiations and discussions. She is now concentrating, full-on, on a campaign to get her vote out. End of story,” the source said. A source close to Beckett confirmed he put forward the idea of choosing a name at random because he believed it would be the best outcome for the union. “Howard has let it be known that he is open to considering all options to secure the future of Unite,” the source said. Negotiations between the left candidates were hastily arranged last week after Coyne received 196 nominations from union branches to make it on to the final ballot. Turner won the most with 525 nominations, Graham surprised many by coming second with 349, while Beckett came third with 328. A victory for Coyne could result in a significant reduction in the influence of the left over the Labour movement. Unite under its current leader, Len McCluskey, has been a strong critic of Starmer’s style and politics, controls votes on the party’s ruling body, and has maintained close alignment with Jeremy Corbyn and his former supporters. Graham’s supporters say she has the broadest support base among Unite’s industrial branches and have said she will disentangle the union from involvement in internal Labour politics. Beckett, the union’s former legal adviser who was recently suspended from Labour for saying Priti Patel should be deported instead of refugees, has been a close aide to McCluskey. He is advocating an increase in the union’s strike fund from £40m to £50m. Turner, who has also been close to McCluskey, was seen as the favourite to win after securing the support of the United Left faction. He has argued for more pragmatism from the union’s leaders. The 2017 battle for the Unite leadership was hugely divisive and led to Coyne being suspended from his position in the union. Coyne was then sacked in June 2017, three months after standing against McCluskey for the union’s leadership. While McCluskey won 59,067 votes (45.4%), Coyne secured 53,544 (41.5%). He has called for the union to focus on its members rather than controlling Labour, and is seeking an independent investigation into the use of members’ money to build a £98m conference centre in Birmingham. Ballot papers are expected to be printed by the end of this week and dispatched by 5 July. The result is due on 26 August.