The minister, however, cautioned that the drilling was being carefully carried out to avoid a cave-in.
Golborne told Xinhua on Thursday that Plan C, which involved an oil drilling rig-421, had completed the installation of its tower and could begin operations Saturday.
"We will begin this week with two drilling machines in the final diameter that allows us to look quite optimistic that we can reach them in a reasonable time. The date remains early November," he said.
Plan A, a slower Strata 950 hydraulic bore, has so far descended only 320 meters through the ground.
Once the hole gets to be 71 centimeters in diameter, the miners will be hoisted up one by one in a steel escape capsule that is still being designed and will be equipped with oxygen tanks and a communications system.
According to technical studies, each rescue will take no more than 15 minutes. Once above surface, the miners will be taken to a nearby field hospital or, in extreme cases, airlifted to a hospital in Copiapo.
The government has refused to estimate the cost of the rescue effort but the drilling alone will cost nearly 5 million U.S. dollars, meaning the overall bill could reach 10 million dollars or more before the miners see sunlight.
Saturday -- the anniversary when Chile declared independence from Spain on Sept. 17, 1810, launching a war they finally won in 1818 --will be the 46th day of the miners' confinement.
Michael Fortt, the chief engineer of the rescuers, said the miners were in good health and that they talk daily with their families.
However, a letter from a miner identified as Daniel Herrera on Thursday warned of a possible rift between some miners and a psychologist responsible for the health of the miners.
The psychologist tried hard to establish telephone conversations with all of the miners but was rejected by several, Herrera said.