The owner of British Airways may bid for Norwegian Air Shuttle, the fast-expanding budget airline.
Buying the airline would allow International Airlines Group to increase its market share amid rising competition from low-cost carriers.
Norwegian said it had not been aware that IAG had acquired a 4.6% stake until media reports on Thursday.
Shares in Norwegian closed 47% higher after news of the bid interest emerged, while IAG fell 1.2%.
Norwegian said it has not held talks with IAG but said the interest "confirms the sustainability and potential of our business model and global growth".
IAG said it had bought a minority stake in the airline with a view to opening talks about a deal.
"The minority investment is intended to establish a position from which to initiate discussions with Norwegian, including the possibility of a full offer for Norwegian," IAG said.
However, it said no discussions have taken place and it had not decided whether to make an offer.
Analysis: Simon Jack, BBC business editor
Norwegian has been ruffling feathers in the aviation market, bringing a budget airline model to the long-haul sector. The industry is divided as to whether it works when you cross the Atlantic.
Norwegian has bet big that it does. Starting life as a short-haul carrier, it has nearly 200 long-range aircraft on order and the legacy carriers have had to respond.
IAG is dabbling with its own offshoot, Level, and BA announced cheaper fares for long-haul passengers not checking in bags and not wanting to choose a seat. Air France's Joon is also trying to cut long-haul costs.
Norwegian is still losing money and its finances are stretched by the number of planes it is buying, but today's announcement from BA suggests Norwegian has proved the concept is sound.
Whether passengers are best served by a legacy carrier swallowing a competitive upstart is another debate.
Norwegian Air has earned a name for its low-cost deals, such as £99 one-way flights from Edinburgh and Dublin to New York.
However, it posted a net loss in 2017 and had to raise fresh funds earlier this year to cope with its rapid expansion and higher fuel costs.
Nevertheless, its move into discount intercontinental flights has shaken up the market and forced bigger rivals such as IAG and Air France to take measures to win back customers.
IAG has already put a toe in the budget long-haul market with Level from Barcelona, while adding European airport slots from failed UK airline Monarch.
IAG chief executive Willie Walsh has long been interested in low-cost long-haul concept long before it set up Level, said Liberum analyst Gerald Khoo.
"This may be an attempt to accelerate its development, while also adding to the scale and reach of [IAG-owned] Vueling in the intra-European market."
This week, BA began selling "Basic" tickets from London to destinations including Boston, Delhi, Dubai, Hong Kong and Singapore.
Fares start from £143, but passengers must pay £60 to check a bag and £20 for seat selection.
Simon Calder, travel editor of the Independent, told the BBC: "The main purpose of this initial move is to get more competitive with Norwegian, which is building an extensive network from Gatwick and poaching passengers from British Airways. Most of the first 10 destinations are on the Norwegian network."