"We are aware of the news reports being circulated about our treasured son and are waiting for confirmation from the government as to the authenticity of these reports," Ed and Paula Kassig said in a statement.
The IS group released a video today claiming the killing, showing a masked militant standing over a severed head whom the militant said was Kassig.
The same video also showed the simultaneous beheadings of at least 18 men described as Syrian military personnel.
"The family respectfully asks that the news media avoid playing into the hostage-takers' hands and refrain from publishing or broadcasting photographs or video distributed by the hostage takers," the Kassig's wrote.
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"We prefer our son is written about and remembered for his important work and the love he shared with friends and family, not in the manner the hostage-takers would use to manipulate Americans and further their cause."
Kassig, a former soldier who was also trained as an emergency medical technician, disappeared from Syria in October 2013.