A spokesman for the NFL said the Falcons have acknowledged a coach asked Ohio State cornerback Eli Apple the question during the NFL Combine.
"We will look into it," Brian McCarthy said.
The Falcons didn't immediately reply to CNN's request for comment, but according to the Atlanta Journal Constitution, head coach Dan Quinn apologized for the question.
"I am really disappointed in the question that was asked by one of our coaches. I have spoken to the coach that interviewed Eli Apple and explained to him how inappropriate and unprofessional this was," Quinn told the newspaper in a statement.
Apple, a redshirt sophomore, was asked by Comcast SportsNet's "Breakfast on Broad" what was the weirdest question he was asked during his interview at the NFL Combine.
Apple replied: "The Falcons coach, one of the coaches, was like, 'So do you like men?' It was like the first thing he asked me.
"It was weird. I was just like, 'No.' He was like, 'If you're going to come to Atlanta, sometimes that's how it is around here, you're going to have to get used to it.'
"I guess he was joking but they just ask most of these questions to see how you're going to react."
The combine is a skill audition and physical evaluation for players who have declared for the NFL Draft, which begins April 28. Apple is a top prospect and a potential first-round pick.
NFL Players Association Executive Director DeMaurice Smith referenced the story on Twitter, saying it was "another dehumanizing moment in NFL Combine history."
Apple had 33 tackles and one interception for the Buckeyes, who finished the season ranked No. 4 in the nation.
This is not the first time an NFL prospect has reported being asked about his sexual orientation.
In February 2013, tight end Nick Kasa, now with the Denver Broncos, told ESPN Radio Denver that at least one team asked him, "Do you like girls?"
"Any team or employee that inquires about impermissible subjects or makes an employment decision based on such factors is subject to league discipline," NFL spokesman Greg Aiello told CNN at the time.
Three years before that, the combine generated controversy when then-Miami Dolphins General Manager Jeff Ireland asked Dez Bryant, now a Dallas Cowboys wide receiver, whether Bryant's mother was a prostitute. Ireland apologized. He is now a scout with the New Orleans Saints.