Reyes, 45, who was described by Politico as a "rising Republican star" was appointed Utah's top law enforcement officer in 2013 after the resignation of John Swallow, then won election the following year and re-election last year.
Swallow, also a Republican, resigned amid a political scandal that alleged bribery and corruption inside his office.
The scandal was exposed in part after Utah businessman Jeremy Johnson, who had close ties to Swallow and his immediate predecessor, former three-term Utah Attorney General Mark Shurtleff, was slapped with federal criminal charges that grew out of the FTC's investigation into his online-marketing company's business practices.
A Reyes spokesman would neither confirm nor deny the report.
"At this time, Sean has not applied for the FTC job, he has not submitted his résumé for the FTC job, nor has he been interviewed for the FTC job," Reyes' political director, Alan Crooks, said. "But the Politico story suggests there are some heavy rumors going around in D.C."
Reyes was at Trump Tower in New York on election night, Nov. 8, 2016.
He talked about the experience of being with the Trump family the next day on KNRS Radio's "Rod Arquette Show" and said he'd been asked by many if he wanted, or was angling for, a job in the new administration.
"Absolutely not. I love this job," Reyes told Arquette. "It's the greatest job I've ever had being the A.G. for the state of Utah. I'm passionate about it, and I will commit that I want to stay here."
Reyes said there was nothing that would lure him way from Utah, but that if he could see a way for Utah to contribute or help Trump in some way, for example aiding in choosing Supreme Court nominees, he would be "excited to serve in that capacity."