Jordan has demanded evidence the pilot, who crashed in Syria on December 24, is alive before freeing would-be suicide bomber Sajida al-Rishawi, who is on death row.
Jordan has offered to free Rishawi, who was convicted for her part in triple-hotel bombings in Amman in 2005 that killed 60 people, if Isis releases the pilot.
The Jordanian Government has been under heavy pressure at home and from Japan - a major aid donor - to save Kaseasbeh as well as Goto.
Isis threatened Kaseasbeh's life, but it was not clear from its latest message if the jihadist group was ready to free him as part of an exchange. Japan, which plays no military part in the fight against Isis, was thrust on to the front line last week when a video appeared of two of its nationals, Goto and Haruna Yukawa, kneeling in the desert.
A masked, knife-wielding militant said Tokyo had 72 hours to pay a US$200 million ($275 million) ransom if it wanted to spare their lives. When that deadline expired, new pictures appeared to show Yukawa had been beheaded, and a voice identifying itself as Goto demanded the release of Rishawi.
- AAP