Sam, a seventh-round draft pick in May, is due to report to the St. Louis Rams' camp Tuesday.
"I wouldn't have taken him," Dungy, the former coach of the Tampa Bay Buccaneers and Indianapolis Colts, told the Tampa Tribune. "Not because I don't believe Michael Sam should have a chance to play, but I wouldn't want to deal with all of it.
"It's not going to be totally smooth ... things will happen."
Dungy, now an NBC commentator, is widely known for his religious beliefs. While coaching the Colts in 2007, he openly supported a proposed gay-marriage ban.
The Tribune story quoted numerous figures from the NFL and the sports world on the impact of Sam's presence with the Rams. Many agreed with Dungy that incidents could arise in the locker room or elsewhere.
"Of course it's naive to think there won't be any problems surrounding Michael Sam," Tampa Bay Rays manager Joe Maddon told the newspaper. "People are going to carry their judgments wherever they go. Once his teammates get to know him, hopefully they'll understand his intentions are to win football games. But you're going to have to put up with a group of people who will try to place their mores on everybody else.
"Over time, that noise will go away. In the meantime, Michael Sam needs to be supported. It always takes a couple of years from that first moment, that seminal moment, for things to be more accepted in sports. I'm saying that five years from now, it'll become part of the fabric, a non-issue."