British Airways' parent company said Thursday it is considering making an offer for the low-priced carrier.
Norwegian shares rose by 40% in early trading upon the news.
It said "no such discussions have taken place to date" and that "no decision" had been taken to make an offer, adding that "there is no certainty that any such decision will be made".
IAG owns airlines Aer Lingus, British Airways, Iberia and Vueling.
Shares in Norwegian soared by almost 48 per cent after it emerged IAG has taken a 4.61 per cent stake in the airline and was considering a full acquisition. It would also put IAG into the pole position in the long-haul, low-priced market, for which Norwegian has been building a large base at London-Gatwick airport. Also, the carrier states that "Norwegian has not been in any discussions or dialogue of IAG about the matter".
Norwegian released a brief statement in which the airline confirms the acquisition of 4.6 percent and affirms that it had "no prior knowledge" of the transaction.
Here in Canada, Norwegian Air filed with the Canadian Transportation Agency to possibly start transatlantic flights from this market starting summer 2018, however on Tuesday it was reported that the airline has pushed back plans for a possible Canada launch until at least spring or summer 2019 due to aircraft delivery delays.
Norwegian has been expanding aggressively, particularly on long-haul routes and, because of the massive expansion, made a loss in 2017 following a profitable 2016.