The mountaineer, who has yet to be identified, died at Camp 4 after falling ill with altitude sickness late Friday as he descended the world's highest mountain.
Indian climber dies after scaling Himalayan peak
"A team member informed us about the death but details of the dead are yet to come," said Mingma Sherpa, Managing Director of Seven Summit Treks.
Unconfirmed reports said the climber was a Dutch national.
"We are now working on bringing the body from Camp 4 to base camp first and then to Kathmandu," Sudarshan Prasad Dhakal, Director General of Nepal's tourism department, said.
Around 330 climbers have successfully scaled Mount Everest this season after two consecutive years of deadly disasters, but two mountaineers have died in the past few days.
A Nepali sherpa guide perished Thursday after he slipped and fell 2,000 metres (6,562 feet) down Mount Lhotse, the world's fourth-highest peak.
Climbers near Everest summit for first time in three years
On the same day an Indian climber died after falling ill while descending from Mount Dhaulagiri, also in the Himalayas.
Nepal issued 289 permits to foreign mountaineers for this year's brief spring climbing season, which runs from mid-April to the end of May, after two consecutive failed seasons.
Hundreds of climbers fled Everest last year after an earthquake-triggered avalanche at base camp killed 18 people.
Only one climber summited the mountain in 2014 after an avalanche killed 16 Nepali guides that year.
Climbers make first winter ascent of Pakistan's 'Killer Mountain' Nanga Parbat
Since the first summit of Everest in 1953, more than 300 people, most of them locals, have died while attempting to scale Everest and Lhotse, which share the same route until Camp 3 at 7,200 metres.
Mountaineering is a major revenue-earner for the impoverished Himalayan nation but last year's earthquake, which killed almost 9,000 people, threatened the future of the country's climbing and trekking industry.
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