Whitby has offered a £50,000 bursary to the Academy to carry out the work, and provide what he described as "a more balanced approach" to the energy debate.
"Before people start investing in new nuclear power stations we need to know if it really is carbon free," Whitby told NCE this week.
He claimed that there was currently no definitive piece of research work carried out to discover the true financial and carbon cost of new nuclear power stations. However, in the debate of energy supply for the UK a wide variation of figures were constantly being quoted.
"What is the actual carbon cost of nuclear?" he said. "What I feel is important is that this work is carried out by an august body like the Royal Academy and not by some other lobby group."
Whitby made his challenge to Royal Academy chief executive Philip Greenish and has a meeting arranged in February to discuss the offer of funding for the work.
He has previously been critical of the Royal Academy's 2004 report into the cost of electricity generation put the cost of nuclear energy for lacking balance. This was carried out by consultant Parsons Brinckerhoff Power.
Speaking to NCE, the chief executive of the Royal Academy of Engineering, Philip Greenish, said that he had not been formally offered any money by Whitby.
"Mark was in communication with me on a separate issue, and in response he said that he had talked to [Royal Scoiety vice-president] Scott Steedman about embodied energy in nuclear generation and suggested we do a study.
"We have not yet been formally offered the money, and neither have I accepted it," he said.
Greenish said that whether he accepted any money would depend on, "a number of other factors. Our simple interest is in producing evidence-based advice. If this is what he proposes, then it could be helpful," he said.