The results will be certified later this week, but the Associated Press reported Monday that Salmon's slim margin will likely overturn the Nov. 7 re-election of Randy Brock, the Republican incumbent.
Salmon is the son of former Vermont Gov. Thomas Salmon.
With Chittenden County, the state's largest county, recording its recount results early Monday, Vermont Secretary of State Deborah Markowitz said it did appear as though Salmon picked up enough votes to win the auditor's seat.
"He will likely be determined the winner by the court," Markowitz said. "There may be a question here or there, but not enough to make a difference."
Washington County Superior Court Judge Mary Miles Teachout will certify the results at a hearing on Thursday at 10 a.m.
With recount results from all 14 of the state's counties now in, Salmon ended up with 111,741 votes, while Brock received 111,637.
Volunteers counted more than 250,000 ballots by hand during the past two weeks in county courthouses across the state.
Salmon lost the Nov. 7 race by 137 votes and requested the recount.
It was the first statewide recount since 1980, and if the results hold, it will be the first in Vermont's history to overturn a certified election result.
Markowitz said Salmon picked up most of his votes through clerical errors in towns where Liberty Union candidate Jerry Levy did not receive any votes.
The votes were counted correctly, but when Levy did not receive any votes, the election workers, late at night, only had three results to transpose to the official tally sheet.
But there were four empty lines on the sheet. Progressive candidate Martha Abbott also had a line on the tally page.
Markowitz said in more than one town, some of Salmon's results were recorded to Levy. She said all of the major errors happened in towns that did not use tabulation machines, but rather counted votes by hand.
"There were 14 here and 40 there, and in an election that is decided by only 137 votes, that makes a difference," Markowitz said.
She said her office is going to work on the vote count system and possibly institute changes for the next election.
Markowitz also said another recount can only be requested if a citizen believes that the recount procedure was flawed.
"Mr. Brock does not have many other options," Markowitz said. "The whole process is nonpartisan. Every ballot was looked at twice by a Democrat and a Republican. The outcome is very precise. There is no place in the law to ask for another recount."
Salmon said he started getting calls from supporters in the Democratic Party late last week and he said he heard about the unofficial results early Monday, but he did not want to claim victory until the results are certified on Thursday.
"There is no victory party planned yet," Salmon said. "I do feel as though the recount was done according to the law by dedicated Vermonters and I will believe in the results when they are released. The right thing to do is wait for the certification."
Salmon said his son had a basketball game Monday that he was still planning on attending.
"We'll let them settle this and certify the results," he said. "Out of courtesy to Mr. Brock and all of the candidates, I do not want to jump the gun."
The race between Brock and Salmon was close throughout election night.
Salmon was barely ahead at the end of the night and Brock pulled ahead early the next day.
Brock also said he was going to withhold comments until Thursday.
He had only heard about the results through calls from the press, and he said there are still a few questions to be answered.
Among the issues that could affect the outcome -- yet again -- are any ballots that were challenged by the recount teams in the 14 counties. It was not immediately clear Monday how many challenged ballots there were.
Windham County Clerk Larry Robinson said there was one challenged vote where a voter had put a mark by two candidates.
He said Salmon picked up about 50 votes when the counting was completed.
Chittenden County Clerk Diane Lavallee said there was one in the Burlington area. The voter had appeared to vote for a write-in, but then never wrote anyone's name. Another candidate's name was circled, instead. She could not recall whether it was Salmon or Brock whose name was circled.
Because there was not agreement on the questioned ballots, Teachout will have to determine the voter's intent or else declare it a spoiled ballot that doesn't get counted.
And Markowitz said there also were about 60 vote-by-phone ballots and provisional ballots that will have to be counted. Those ballots are counted by the Secretary of State's Office and Markowitz said they were equally divided between Brock and Salmon.
She said Teachout will have to determine whether the challenged ballots would make a difference. "If all the challenges go to Brock, or they're not counted, will that matter in the outcome?" Markowitz said.
Washington County Clerk Claire Mee said she did not know how many challenged ballots there were either.
Brock said all eyes will be on the Washington Superior Courthouse Thursday.
"We have already seen in this race that is very unwise to make a decision based on unofficial results," Brock said. "There are still a number of issues that will be reviewed in the recount process and we do not know what impact, if any they will have on the results. We will have to wait and see."