International Consolidated Airlines Group (IAG) confirmed that it was considering making an offer for the rival carrier after taking a 4.6 per cent stake in the company.
Shares in Norwegian Air rocketed 18 per cent in Oslo following news of IAG's interest.
The shareholding "is meant to establish a position from which to initiate discussions with Norwegian, including the possibility of a full offer for Norwegian".
IAG says no official discussions have taken place, and the company emphasized that it hasn't decided whether it will make an offer. March also saw low-priced subsidiary LEVEL begin a new route from Barcelona to Boston, and in July the airline will start operations from Paris-Orly to Montreal, New York (Newark), Guadeloupe and Martinique. The Scandinavian airline added that "it has not entered into any discussion or dialogue with IAG about matter", although it indicated that "IAG's interest in company confirms sustainability and potential of our business model and our Global growth ".
Adding Norwegian's short-haul operations in Europe to Vueling would create a budget carrier better placed to compete against the continent's two biggest low-priced airlines Ryanair and easyJet. Some of the airline's top competitors in the budget airline industry include Ryanair and EasyJet, which are based in Ireland and Luton, England, respectively.
As well as British Airways, IAG also owns Spanish low-priced airline Vueling and recently launched a budget long-haul operator dubbed Level.
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Shares in Norwegian, a stock which this year has been pounded over worries about its profitability, surged 37% on the news.
There will be no buying Norwegian on the cheap, however, said SEB analyst Jo Erlend Korsvold.
Last month Aer Lingus launched its 14th transatlantic route with service between Dublin and Philadelphia that will be followed by a new Seattle link next month.
"Willie Walsh has always been interested in the low-priced long haul concept, long before the creation of Level".
IAG's interest in Norwegian would see a wave of consolidation in European air travel which started past year extend its reach to long-haul travel.