Officials have declined to comment but a news conference is scheduled to take place shortly.
Water and time remain the two difficulties facing rescuers.
However experienced cave rescue experts consider the underwater rescue a last resort, especially because the boys are not trained in diving.
A multinational rescue operation led to their being found safe on a dry ledge, but their extraction through narrow, still-flooded accessways has posed a unsafe challenge, especially amid concern for their health after being trapped without light or nourishment for so long.
The suggestion that the trapped team might have to wait months inside until a safe way out is available - as was the case in 2010 with Chilean miners trapped underground - has been met with little enthusiasm.
Over the past couple of weeks, officials had been exploring different ways to get the boys out, including drilling down into the cave or looking at other entrances to the mountainside.
A military operation - called "Wild Boar" - has commenced to rescue the boys, aged 11 to 16, and their 25-year-old coach.
Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days.
The 12 Thai boys and their soccer coach will be accompanied by divers and will have to navigate tight passageways filled with muddy water as part of their rescue mission.
"Today is the peak of our readiness", said Narongsak Osottanakorn, a former provincial governor who is leading the rescue efforts.
The handwritten letters from the group were handed to British divers on Friday and released on the Thai Navy Seal Facebook page today. Do take good care of yourself. The letters, carried by divers making 6-hour trips in each direction, were the first direct communication between the parents and their sons.
Chiang Rai province Governor Narongsak Osotthanakorn has said it is too risky for the Thai soccer team to be extracted from the cave for now, while also confirming fresh oxygen will be pumped in.
The priority, Pasakorn and army officials say, is getting oxygen to the boys as it slowly runs out.
Narongsak acknowledged that the air supply inside the cave is "a big problem".
"We estimate that they are 600 metres down, but we don't know the exact target", he said.
Rescuers have been pumping water around the clock in an effort to drain the deluged cave enough so that the boys can safely exit the cave. The diver was working in a volunteer capacity and died during an overnight mission in which he was placing oxygen canisters along the route divers use to get to the children, Arpakorn said.
Narongsak said Saturday that experts told him water from new rain could shrink the unflooded space where the boys are sheltering to just 10 square meters (108 square feet). The American behind Tesla cars has stepped in to help the dozen lads with his firm the Boring Co.