Adam Schiff, the top Democrat on the House intelligence committee, confirmed the line of inquiry at a breakfast with reporters today, but declined further comment.
ABC News first reported that US officials believe Mueller, whose death was announced in February, spent time in the custody of the Tunisian Islamic State finance man known as Abu Sayyaf.
A US official today said Sayyaf's real name was Fathi ben Awn ben Jildi Murad al-Tunisi.
Murad was killed Friday during a rare ground operation in Islamic State-held territory in Syria by Delta Force operators.
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Intelligence analysts are also sifting through reams of electronic data seized at the site, the official said.
Murad had a number of aliases, the US official said, but officials believe that Murad is his real name. Murad is believed to be the Islamic State's head of oil operations.
Both officials spoke on condition of anonymity because they were not authorized to discuss the matter publicly.
The Islamic State group said Mueller was killed in a Jordanian air strike, but U.S. Officials have cast doubt on that assertion.
"We are currently debriefing the detainee to obtain intelligence about ISIL operations," she said. "We are also working to determine any information she may have regarding hostages - including American citizens who were held by ISIL.