Carsten Spohr told the German newspaper Suddeutsche Zeitung that there was “a new wave of consolidation approaching”, adding that Lufthansa was “in contact with Norwegian”.
He said: “Takeovers are always a question of strategic value, the price and anti-trust. There are no easy answers.”
Lufthansa’s interest in Norwegian Air comes months after IAG, the owner of British Airways, bought a 4.6% stake in the Nordic carrier.
IAG has since made two further offers for the airline, both of which were rejected.
Norwegian Air’s rapid expansion, with flights costing as little as £99 from Edinburgh and Dublin to New York, has attracted the attention of several suitors. It carries more than 30 million passengers a year, including 5.2 million from the UK.
A Norwegian Air spokesperson said the firm had “received enquiries from several parties following the International Airlines Group’s (IAG) acquisition of 4.6% of the shares in the company”.
They added: “These parties have expressed indicative and preliminary interest in share acquisitions, mergers, structured transactions, financing of the group and various forms of operational and financial cooperation.
“Norwegian believes that interest from several parties demonstrates the attractiveness of our business.”
As well as British Airways, Anglo-Spanish firm IAG also owns Aer Lingus, Iberia and Vueling. It also recently launched a budget long-haul operator called Level.
Lufthansa owns its own low-cost brand Eurowings.
Consolidation in the European airline industry has been sparked by rising fuel prices and the collapse of Air Berlin and Monarch.
Norwegian’s shares rose 9.8% to NKr273 (£25.15) in early afternoon trading on the Oslo Stock Exchange. Deutsche Lufthansa’s stock slipped 0.6% in Frankfurt and IAG rose 0.2% to 715p in London.