The Tokyo-listed stock jumped 27.77% to finish at 230 yen, its maximum allowable single-day gain, on the report in Japan's leading Nikkei business daily.
The report, which cited unnamed sources, said AirAsia was in talks with its lenders over a possible takeover bid for money-losing Skymark.
In a statement, AirAsia dismissed the story as "speculation" and "just another industry rumour".
"Never seen such rubbish. AirAsia has no interest in Skymark in Japan," AirAsia chief executive Tony Fernandes wrote on Twitter.
"There have been no discussions with Skymark," he added.
The putative takeover target also questioned the report.
"We're not aware that there is any truth in what has been reported," Skymark said in a statement.
In the wake of its bitter split last year with All Nippon Airways (ANA) over a budget carrier joint venture, AirAsia has announced it would jump back into the Japanese market in a tie-up with e-commerce giant Rakuten.
The Nikkei had said the low-cost carrier might create a new local subsidiary, backed by Rakuten, to launch the bid for Skymark to get around restrictions on foreign ownership in Japanese airlines.
Skymark was born out of deregulation measures in the 1990s which were aimed at challenging ANA and rival Japan Airlines' control of the market.
But the carrier has been reporting ballooning losses as new entrants into the budget sector hurt its business.
The airline was sideswiped when Airbus last month said it had cancelled a US$2.2-billion jet order with the carrier, apparently over concerns about getting paid.
Skymark shares had lost more than 40% at one stage following the collapsed deal.
The company said the European aviation giant had threatened it with "overpriced" penalties and called on it to merge with a bigger airline, a proposal which Skymark's top executive flatly rejected.
The Nikkei report also said AirAsia, a major Airbus customer, had approached the plane maker about reducing the cancellation penalties.
Skymark has said it was mulling the cutting of unprofitable routes and borrowing more money from its banks to stay afloat.