Discussions with authorities were underway to find Paresh Chandra Nath (58) and Goutam Ghosh (51), said Wangchu Sherpa, the managing director at Trekking Camp Nepal.
Nath and Ghosh were near the summit of the 8,848-metre peak on Saturday when they lost contact with the rest of the four-member team, all of whom were Indians.
One of the team members Subhash Pal died after falling ill on Sunday. The fourth woman member Sunita Hazra was rescued and taken to hospital.
In a status report on Monday, the Indian Embassy said it was in constant touch with authorities concerned with rescue operations, as well as Deepankar Ghosh, an official from the Government of West Bengal.
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The embassy said it has made arrangements for hospitalisation of rescued climbers and for the transportation of mortal remains of those dead to India, the Himalayan Times reported.
Five people have died so far during this Himalayan climbing season, which saw about 400 mountaineers summit the world's highest peak, officials have said.
More than three dozen other climbers have developed frostbite or become sick near the summit in the past few days.
Nearly 40 climbers including an Indian woman have developed frostbite during this Himalayan climbing season
Last year, devastating earthquake caused the climbing season to be canceled and climbing attempts were largely abandoned in 2014 after an avalanche above the base camp killed 16 Sherpa guides.