Lay and Skilling, who also served as CEO, were convicted in May 2006 for their role in the accounting fraud that led to the collapse of Enron in 2001. The bankruptcy erased billions in investors' money and wiped out the pensions of thousands of Enron employees.
The custom-made desks with "an elegant Makore Pommelle veneer" have a minimum bid of $25,000 each, which so far has not been met. The auction began on Friday and runs for 10 days.
Skilling is now serving a 24-year prison term in Minnesota, while Lay's conviction was vacated following his death from a heart attack in July 2006.
Numerous Enron-branded items are currently for sale on online auction service eBay, ranging from coffee mugs to stock certificates. The company's twirling "crooked E" logo from its headquarters in downtown Houston sold for $33,000 at auction in 2002.
The desks were donated by a member of the group which bought one of Enron's two towers in 2003, a spokeswoman for the charity said.