A Nepalese friend of Ryan Sean Davy said that the climber was being questioned by tourism officials.
He is due to appear in court on Wednesday where he is expected to receive a heavy fine.
Friends say Mr Davy has no cash, which is why he mostly travelled on foot.
"He is in good heart although worried about his finances and the scale of the punishment he will receive," Mr Davy's Nepalese friend Mohan Gyawali told the BBC.
US-based South African Mr Davy, 43, says he climbed alone to a height of 7,300m (24,000ft) before being found hiding in a cave by officials who confiscated his passport because he did not have a permit to climb Everest.
He has apologised but complained of being treated harshly by officials. It is extremely rare for someone to attempt climbing Everest by themselves.
The overwhelming majority of climbers only tackle the highest mountain in the world with the help of at least one guide and a well-equipped support team at base camp.
"I have no idea of the outcome regarding my Everest no-permit climb," Mr Davy posted on Facebook on Tuesday
Mr Gyawali said that the climber made his way back to Kathmandu using the same route from the base camp that Sir Edmund Hillary and Tenzing Norgay followed in 1953 when they became the first people to climb the mountain. The route goes through the small mid-hill town of Jiri.
Nepal relies heavily on income generated from Everest expeditions and some believe the authorities will want to make an example out of Mr Davy to deter other climbers from dodging the permit fee.
Mr Davy said on Facebook: "Expedition companies have no time for wannabe Everesters with no money so someone turned me in."
The climber said he could expect to spend time in jail in addition to a fine of $22,000.
A man who tried to climb Everest in Nepal without paying the $11,000 permit fee has been arrested in Kathmandu after walking most of the 154km journey from the mountain's base camp.