The workers, who were building the tunnel, were trapped when part of it caved in due to a landslide.
Officials have been able to establish contact with the men and have been providing them with food, water and oxygen while they try to get them out.
They say they expect to rescue the workers by Tuesday night or Wednesday.
On Tuesday morning, the state government said rescue teams were "preparing to drill and insert a metal pipe of 900mm diameter in the part of the tunnel blocked by debris" to reach the workers.
Officials hope the men will be able to squeeze through the narrow pipe to safety.
The tunnel in Uttarkashi district is part of the federal government's ambitious highway project to improve connectivity to famous pilgrimage sites in Uttarakhand. The mountainous state, where several Himalayan peaks and glaciers are located, is home to some of the holiest sites for Hindus.
The accident occurred at 05:00 local time (23:30 GMT) on Sunday when a portion of the Silkyara tunnel, around 200m away from its opening, collapsed while the workers were inside, senior police official Arpan Yaduvanshi told BBC Hindi.
A landslide nearby caused heavy debris to fall on the tunnel, leading to its collapse. The mounds of debris cut off oxygen supply to the workers.
Authorities said they established contact with the trapped men on Sunday night using walkie-talkies.
A pipeline, which was laid for supplying water to the tunnel for construction work, is now being used to supply the trapped men with oxygen, food and water, they added.
Rescuers will have to dig through several metres of debris before they can start the evacuations. Excavators and other heavy machines are bring used to dig through the debris.
State Chief Minister Pushkar Singh Dhami said national and state disaster relief teams were working together on rescue efforts.
"All the workers trapped inside the tunnel are safe and every effort is being made to get them out soon," a statement from his office said.
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Rescuers are racing to save 40 workers trapped inside a collapsed tunnel in the northern Indian state of Uttarakhand since Sunday morning.