In a statement Tuesday, the Nasdaq said a Wall Street Journal story that its chief executive Robert Greifeld had approached the NYSE with the offer was "based on rumors and speculation" and "has no basis in fact."
"We don't make comments on market speculation," Nasdaq spokeswoman Sylvia Davi told CBS Radio News.
"We don't make comments on rumors and speculation," echoed the NYSE.
The newspaper, citing unidentified sources, also reported that the concept is at a very preliminary stage and no formal proposal has been made.
The speculation comes during challenging times for both institutions.
The NYSE is dealing with criticism that its open-auction style trading system is antiquated, on the heels of a pay scandal sparked by former chairman Dick Grasso's $188 million compensation package.
The Nasdaq, which rode high on booming technology stocks during the late 1990s, has struggled to recover from the collapse of many dot-com firms beginning some four years ago.
Any such merger would be subject to approval by the federal Securities and Exchange Commission since both entities are classified as self-regulatory organizations.
A merger between the nation's two biggest markets would likely be welcomed by Wall Street firms, which could potentially save money by combining their trading desks and reducing their membership fees.
The proposal drew immediate criticism from analysts. Jodi Burns, a market analyst with the consulting firm Celent, told CBS MarketWatch the proposal was akin to "breeding a dog and a cat." A merger would also effectively wipe out meaningful competition by creating a giant with almost a complete monopoly.
"There are no synergies," she said. "The technology at the Nasdaq would wipe out the specialist model. It's not simply splicing the best of Nasdaq and the best of the NYSE. The two market structures are incompatible."
That was the story when the NYSE and American Stock Exchange considered a merger, said Michael Goldstein, a former NYSE visiting economist and current member of an economic advisory panel to the Nasdaq.
However, it would not be unprecedented to have a single stock exchange in the United States.
"It reverts to the model we had in the 1920s," he said. But it doesn't make sense from a market systems standpoint."