Al-Kasasbeh was seized by Islamic State militants after his jet crashed in north east Syria in December during a bombing mission against the militants.
A video released by Islamic State media channel al-Furqan appeared to show al-Kasasbeh being burned alive.
The head of the Jordanian armed forces told al-Kasasbeh’s family that he had been killed, Reuters reported.
The date of the murder is unclear, with Jordanian state television reporting that the pilot was killed a month ago on 3 January.
The White House said that it was aware of the video, and was verifying its contents.
The Jordanian authorities said tonight that they will execute “within hours” an Iraqi woman the government had sought to exchange for the pilot. “The decision has been taken to implement the death sentence against the Iraqi convict and others,” the source told Reuters.