Mr Sotloff, 31, disappeared in Syria in 2013. He appeared at the end of a video last month which showed fellow US journalist James Foley being killed.
A militant in the latest video also threatens to kill a British hostage.
Mr Sotloff's family said they were aware of the video and were "grieving privately".
After Mr Foley's death, Mr Sotloff's mother appealed to IS leader Abu Bakr al-Baghdadi to save her son's life.
White House spokesman Josh Earnest said US officials were checking the reports.
The US has recently carried out dozens of air strikes against IS targets in Iraq.