Suggestions have included teaching the boys how to dive, and waiting until the waters subside. They've practiced wearing diving masks and breathing, in preparation for the possibility they may have to dive.
"No, not today", Narongsak Osottanakorn, the governor of Chiang Rai province, said after being pressed by reporters on rescue efforts.
Authorities say that they remain undeterred by the death of the rescue diver, and will continue the rescue mission as planned.
One reason the team can not yet be evacuated is that rescuers were also still searching for three more wetsuits with a thickness of five millimeters, the official, who has direct knowledge of the operation, told CNN. Levels in the area where the boys are trapped dropped from the usual 21% to 15%, authorities said.
In a post on Wednesday, Samarn uploaded pictures of himself in action with a rescue team, both outside and inside the Tham Luang cave.
On the surface, a huge military and civilian rescue operation is racing against the clock to bring the boys to safety.
With murky water rushing through the passageways and rescuers are concerned that having the boys dive out is a unsafe option.
But rescue officials fear their options are running out given fresh monsoon rains are forecast for the coming days.
Billionaire inventor and entrepreneur Elon Musk said engineers from his SpaceX & Boring Co. were headed to Thailand to see if they could help.
"At first we thought we could sustain the kids' lives for a long time where they are now, but now many things have changed", said R Adm Arpakorn Yookongkaew, the Thai navy Seal commander.
Chiang Rai provincial Governor Narongsak Osatanakorn previously said he asked the SEALs in charge of extraction plans to estimate what sort of a risk would be involved to bring out the boys and their coach even though they weren't 100% ready for a risky dive.
But he indicated that further downpours might force their hand and speed up attempts to extract them despite the dangers of carrying out such a gargantuan effort.
The boys have been trapped in a complex cave system in Chiang Rai in northern Thailand since June 23. They were found on Monday by Thai Navy SEALs and two British diving experts.
A daunting task now awaits both the boys - aged between 11 to 16 - and their rescuers.
Few of the boys are able to swim, and none of them have any diving experience.
Former Sgt. Saman Kunan, a Thai ex-SEAL, died at 2 a.m. Friday (2 p.m. Thursday ET), as he returned from an operation to deliver oxygen tanks to the cave where the boys are located. The diver, the first fatality of the rescue effort, 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 reach the children, Arpakorn said.
Volunteers have been descending on the cave site to join the multinational rescue team, which includes Australian police, USA military personnel and British cavers as well as more than 1,000 Thai army and navy personnel. Thai social media filled with tributes to the fallen hero.
Each diver reportedly needs to carry three heavy oxygen tanks to the boys' cave but the path is treacherous, winding, and long, taking skilled divers around five hours each way.
They also can't swim and have zero diving experience, making a rescue very risky.
Their ordeal has gripped Thailand, with the nation holding its breath for their safe escape.
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