IS, in a video released yesterday, threatened to kill airman Maaz al-Kassasbeh and Japanese hostage Kenji Goto unless would-be suicide bomber Sajida al-Rishawi is freed within 24 hours.
"Jordan is ready to release the prisoner Sajida al-Rishawi if the Jordanian pilot is freed unharmed," Jordanian state television quoted a government spokesman as saying.
"From the start, the position of Jordan was to ensure the safety of our son, the pilot Maaz al-Kassasbeh," it added.
It made no mention of Goto.
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Tokyo has been urgently seeking Jordan's help since an IS video released at the weekend said another Japanese hostage, Haruna Yukawa, had been beheaded.
Japan has sent Deputy Foreign Minister Yasuhide Nakayama to Amman to head an emergency response team.
Rishawi has been on death row since 2006 for her part in triple hotel bombings in Amman that killed 60 people.
Kassasbeh was captured on December 24 after his F-16 jet crashed while on a mission against the jihadists over northern Syria.
Jordanian officials have noted that while the IS video threatened Kassasbeh's life, it only mentioned freeing Goto in exchange for Rishawi.