American officials said they were urgently looking into the reports of Mueller's death.
Bernadette Meehan, the spokeswoman for President Barack Obama's National Security Council, said the White House has 'not at this time seen any evidence that corroborates' the claim.
'We are obviously deeply concerned by these reports,' she added.
White House spokesman Eric Schultz told reporters traveling with the president to Indiana on Friday that the U.S. does coordinate with the Jordanian air force on airstrikes.
He wouldn't say whether the U.S. was aware of the hostage's location.
The ISIS statement could not be independently verified but initially appeared on a militant website commonly used by ISIS and was also distributed by ISIS-affiliated Twitter users.
If her death is confirmed, she would be the fourth American to die while in the captivity of the Islamic State militants.
Three other Americans, journalists James Foley and Steven Sotloff and aid worker Peter Kassig were beheaded by the group.
Jordan, which is part of a U.S.-led coalition bombing Islamic State group targets in Syria, stepped up its attacks after ISIS announced it had killed a captive Jordanian pilot.
The Syrian government said yesterday that dozens of Jordanian fighter jets had bombed Islamic State training centers and weapons storage sites. It did not say where the attacks occurred.
There was no word from the Jordanian government on whether its planes had struck Raqqa today although unverified reports on social media claimed the city had been hit multiple times.
Miss Mueller had been working in Turkey assisting Syrian refugees, according to a 2013 article in her local newspaper. She told the paper that she was drawn to help with the situation in Syria.
‘For as long as I live, I will not let this suffering be normal,’ she said.
‘It’s important to stop and realize what we have, why we have it and how privileged we are. And from that place, start caring and get a lot done.’
In a statement today, her family told US radio broadcaster NPR that Miss Mueller had spent her adult life 'travelling the world and helping those in need.'
They said: 'After graduating from college, she spent more than one year living and working with humanitarian aid groups in northern India, Israel and Palestine.
'She returned home to Arizona in 2011, and worked for one year at an HIV/AIDS clinic while volunteering at a women's shelter at night.
"It’s important to stop and realize what we have, why we have it and how privileged we are. And from that place, start caring and get a lot done"
Kayla Jean Mueller