Sharon Graham is said to be “confident” of winning the contest to be the next head of Unite in what would be a surprise defeat for Steve Turner, the candidate favoured by the union’s current general secretary, Len McCluskey.

Graham’s team issued a statement on Tuesday saying they were certain of victory, on the basis of the preliminary results observed after about 10% of ballot papers were opened for sampling purposes.

The union says it plans to announce the official result on Thursday, but the candidates – Graham, Turner and Gerard Coyne – expect the name of the winner will emerge before then and that counting could finish on Wednesday afternoon.

Unite is the country’s second largest union, and the biggest donor to the Labour party. For the past 10 years, it has been led by McCluskey, a supporter of Jeremy Corbyn who has been arguing for Labour to reject Blairism and adopt a leftwing economic agenda.

McCluskey explicitly endorsed Turner, Unite’s assistant general secretary, as his successor, and Turner was seen as the favourite in the contest. His defeat would probably be welcomed by the Labour leader, Keir Starmer, who, like several of his predecessors, has regularly been criticised by McCluskey.

One source claimed on Tuesday that early sampling from the ballot papers showed Graham heading for about 37% of the vote, with Turner and Coyne both on approximately 31 to 32%. The source claimed those figures were based on a representative sample, and that they should provide a reliable guide to the final result.

A spokesperson for Graham’s campaign said: “The sampling of the vote is ongoing. The more it goes on, the better it is looking for us. Of course, we will only get the result when the individual count is finished tomorrow. But we are confident Sharon is going to win it.”

Coyne, who launched an unsuccessful challenge against McCluskey for the leadership in 2017, was the most “centrist” of the three candidates in the contest this summer, and has been described as the one most favoured by Starmer – although Starmer himself has not publicly expressed a view on the outcome.

Graham, like Turner, is a full-time Unite official and a leftwinger. But in her campaign she said she is “not interested in the internal game playing within a political party” and that she wants to focus on workplace issues instead.

More than 1 million Unite members were eligible to vote in the contest, but only about 124,000 ballot papers were returned – a turnout of approximately 12%.

Graham would be the first woman to lead Unite and it is thought that this boosted her appeal in the election – about 290,000 Unite members are women.

Graham also won credit with some members for refusing to pull out so that the left could unite behind a single candidate. Howard Beckett, a Unite official who has been vehemently critical of Starmer, did withdraw and endorse Turner, but this move led to questions being raised about how much power Beckett would be allowed to wield in the union in the event of Turner winning.