Shailendra Kumar Upadhyaya died on Monday afternoon, hours after arriving at camp one in his record attempt, the official told AFP by telephone from Everest base camp. The cause of his death is not yet known.
Upadhyaya had said he wanted to raise awareness about the capabilities of elderly people by scaling the world's highest peak, which has claimed the lives of hundreds of mountaineers.
"The former minister died at around 4:00 pm Monday," government official Tilak Pandey said.
If he had succeeded, Upadhyaya would have become the oldest person to reach the top of Everest, beating current record holder Min Bahadur Sherchan, who scaled the mountain at the age of 76 three years ago.
Around 3,000 people have climbed Everest since Edmund Hillary and Tenzing Norgay became the first people to conquer the 8,848-metre (29,028-foot) peak in 1953.
May is considered the optimum time for climbing in the Nepal Himalayas and around half a dozen people, most of them Nepalese, have reached the top so far this year.
Hundreds more are on the mountain waiting for the right conditions to launch their attempt on the summit.