Amcu's Mpumalanga secretary, John Sibiya, said on Thursday that rescuers were within a whisker of finding the three people trapped in the Lily Mine.
The workers have been trapped since 8:40 on Friday, February 5, when the lamp room - a converted shipping container - where they were on duty, collapsed into an 80m hole.
Sibiya said the rescue team had found the tyre that was close to the container containing the trapped miners - two women and a man.
The tyre provides a glimmer of hope of finding the three, but there were still rocks blocking the way.
He said the rescue team, together with Sasol, was working to ensure that there was not a potentially dangerous blast when they moved the rocks.
Amcu president Joseph Mathunjwa spent the whole night underground on Tuesday to assist in the search, and only came out at 06:15 on Wednesday.
"The human body needs oxygen, food and water to survive and the longer they remain trapped, the slimmer the chances of them being found alive," said Mathunjwa.
He said they were keeping the faith and praying with the families and community members for the safe return of the trapped miners.