According to media reports, HNA was interested in purchasing a 35 percent stake in Cargolux Airlines International SA, one of Europe's largest all-cargo airlines, in 2012.
But HNA denied any plans for that acquisition.
An unnamed official from the group said the companies may have been in exploratory contact.
"Many foreign companies approach us for a deal, but we choose what companies we will buy," Chen said.
The target companies must be able to help improve HNA's competitiveness and expand its market share, he said.
In addition, the companies must be able to be integrated into HNA, not just in business terms but also in culture, he said.
Aigle Azur is a good example, as it helped HNA acquire a new Paris-Beijing route operated by the French airline.
"We expect to launch the Paris-Beijing route this year, as we are only waiting for approval to fly in Russian airspace," said Wang Yingming, president of Hainan Airlines Co Ltd, the aviation subsidiary of HNA Group.
The company also said the return of the Boeing 787 Dreamliner aircraft will help expand its global network.
The Dreamliner was back in the air on Sunday after a three-month grounding for battery problems.
"The aircraft will fly in China in two months," said Chen Wenli, a director of HNA Group.
The company ordered 10 Boeing 787 aircraft which new aircraft will work on its Beijing-Chicago route, due to be launched in September.
"The Seattle and Toronto routes also may use the Dreamliner," Chen Wenli said.
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