"IAG confirms that no such discussions have taken place to date, that it has taken no decision to make an offer at this time and that there is no certainty that any such decision will be made," IAG said in its statement.
Norwegian's shares, temporarily halted after the IAG news, leaped 39 percent to 250 crowns when they resumed trading, valuing the company at 9.5 billion Norwegian crowns ($1.22 billion).
IAG, formed in 2011 by the merger of traditional flag-carriers British Airways and Iberia, has under CEO Willie Walsh recently embraced budget flying, buying Spanish budget airline Vueling in 2015 and setting up its own long-haul low-cost carrier last year.
Norwegian meanwhile has been the trailblazer of low-cost long-haul flying in Europe, undercutting rivals on trans-Atlantic ticket prices, but expanding at a rate which has left it under pressure to control costs and shore up its balance sheet.
Last month it raised $168 million in a share sale after warning of a larger than expected first-quarter loss.
Norwegian said in its statement on Thursday that it had no prior knowledge of IAG's actions, but welcomed the investment.