Samsung recalled the devices last week over battery issues.
US authorities have warned airline passengers not to turn on or charge their Samsung Galaxy Note 7 phones when on board a plane, following reports of devices catching fire.
The Federal Aviation Administration (FAA) also advised passengers also not to stow them in any checked baggage.
Samsung suspended sales of its Galaxy Note 7 last week after a battery issue caused the devices to catch fire.
US airlines said they were reviewing the recommendation made by the FAA.
Delta Air Lines spokesman Morgan Durrant said: "Delta is in constant contact with the FAA and other bodies in its run of business as a global airline.
“We will comply with any directive and are studying this matter. Safety and security is always Delta's top priority.”
The US trade group Airlines for America said it was closely monitoring the issue.
An Airlines for America spokesperson said in a statement, "Each individual carrier makes determinations, in compliance with FAA safety rules and regulations, as to what is permitted to be carried on board and in the cargo hold.”
Apart from US airlines, several Australian airlines such as Qantas, Jetstar, Virgin Australia, and Tiger Airways have banned passengers from using Galaxy Note 7 smartphone in-flight.
The International Air Transportation Association said: “Although Samsung is the most recent company advising of faulty devices, others have issued similar recalls and warnings regarding lithium batteries in laptops over the last 12 months, so the industry is familiar with and equipped to manage such situations."
Samsung is working with suppliers to identify affected batteries in the market.
Galaxy Note 7, an update to the company’s flagship phablet line, was unveiled in August. It is a productivity-driven device, which carries new security features such as an iris scanner.