Min Bahadur Sherchan, a former British Gurkha soldier, was trying to reclaim the record from Japan's Yuichiro Miura, who climbed Everest aged 80 in 2013.
Mr Miura broke Mr Sherchan's own record set as a 76-year-old in 2008.
It comes a week after Swiss climber Ueli Steck, 40, died as he prepared to climb the mountain.
Mr Sherchan died at base camp on Saturday afternoon, officials at Nepal's tourism office said. Doctors suspect he suffered a heart attack, the Kathmandu Post newspaper reported.
His long rivalry with Mr Miura - a year his junior - included a 2013 attempt to reclaim the record aged 81 that had to be abandoned after late spring weather conditions worsened.
In 2015 he was on his way to base camp for another attempt when a devastating earthquake struck the country, forcing him and many other climbers to abandon their plans.
"I want to climb Everest to set a record so that it will inspire people to dream big," he told German news agency DPA in March. "This will instil a sense of pride among old people like me."
"My climb will demonstrate that age doesn't stop you from realising your goal."
Mr Sherchan began climbing in 1960, when he ascended Mount Dhaulagiri, the world's seventh-highest mountain at 8,167m (26,795 ft), the Telegraph newspaper reported.
However he was already 72 when he thought about climbing Mount Everest. To prepare, he walked 1,200km (745 miles) across Nepal in 2003, DPA said.
He told DPA that his inspirations were famous Nepali Sherpas Tenzing Norgay - who first reached the top of Mount Everest with Sir Edmund Hillary in 1953 - and Apa Sherpa, who has climbed the mountain the most times.
Mr Sherchan's guide, Shiva Sapkota, told DPA that he had been in good physical health but had not spent time at high altitude since 2015.
An 85-year-old Nepali man who was attempting to become the oldest person to climb Mount Everest has died at base camp, Nepali officials say.