Southwest issued a travel advisory about the Galaxy Note 7 in September and asks all passengers to follow the Department of Transportation's Safety Requirements: Turn off the device, disconnect from chargers, close all applications, protect the power switch and keep the phone in a carry-on or on their person.
There have been reports that the two handsets will be ready to receive the Nougat treat in this fourth quarter, but there has been little information to back this up.
Green had reportedly powered down the phone for takeoff, an account The New York Times confirmed through other eyewitnesses.
This comes after the handset made an appearance on benchmarking website - Geekbench - with Android Nougat installed.
The smoking phone came to Green's attention when he dropped it on the carpet and noticed smoke coming out of the device.
On October 5, passengers traveling from Louisville to Baltimore were evacuated while still at the gate after a Samsung Galaxy Note 7 smartphone (one with a supposedly safe battery) caught fire. A United Kingdom recall is well underway too, and Samsung has reportedly warned users of the phone in France that their devices could be "turned off", if they don't return them as part of the recall.
The Southwest Airlines plane, which was still on the runway at Kentucky's Louisville International Airport, had to be immediately evacuated.
It began to overheat in the owner's pocket, emitting a "thick grey-green angry smoke".
Following yesterday's incident, Samsung said: "We are working with the authorities and Southwest now to recover the device and confirm the cause".
India's civil aviation regulator last week lifted the restrictions on in-flight use of the new Samsung Galaxy Note 7 smartphone - but only those purchased after September 15.
"A photograph of the box shows the black square symbol that indicates a replacement Note 7 and Green said it had a green battery icon", The Verge reported, adding that Green has now bought an Apple iPhone 7.
Some 60 percent of USA consumers had swapped their devices for replacements by the end of last month.