Jones is in his seventh season as SMU's head coach. The Mustangs are in the American, one of the non-Power Five leagues. The others are the Mid-American, Mountain West, Sun Belt and Conference USA.
"I think the have-nots [non-Power Five leagues] should go ahead and move to the spring just like the USFL did," Jones told WDAE-AM on Thursday. "I think that there's an opportunity to do a complete other side of that division and I think that if we don't think that way as a group of have-nots, we're going to get left behind."
Commissioners Mike Aresco, of the American, Craig Thompson, of the Mountain West, and Jon Steinbrecher, of the MAC, each told ESPN that they have "no interest" nor do they even expect to consider moving from the fall to the spring.
"We have no interest in doing that and have no plans to discuss or look into it," Aresco told ESPN. "Our position is clear. We are an integral part of the fabric of FBS college football.
"Our conference is and will be extremely competitive and our goal is to play at the highest level, compete for playoff and host bowl spots and challenge the Power Five. We want to be in the power conference conversation and, sooner than later, be regarded as the sixth power conference."
Last season AAC champion UCF upset Big 12 champion Baylor in the Fiesta Bowl. In the final AP Poll, the AAC had two teams finish in the Top 15 -- the same number as four of the Power Five leagues (ACC, Big 12, Big Ten and Pac-12).
Steinbrecher also dismissed Jones' idea.
"I have not reviewed this concept with our membership but I cannot imagine we would support such a concept," Steinbrecher said. "We look forward to competing in the fall."
Added Thompson: "There is no chance."
Jones told the Tampa, Florida, radio station if they moved to the spring that in "five-to-seven years, possibly, the public would demand to have the two leagues play, just like I think the USFL had in mind, originally, of the winner of the USFL playing the winner of the National Football League."
There obviously would be a myriad of obstacles to overcome with moving to the spring, including the recruiting and academic calendar, uncertainty of bowl games for non-Power Five leagues, not participating in the new College Football Playoff and NFL draft preparation. Those leagues would also lose the tradition of playing in the fall.
Jones admitted "all those things would have to be figured out," but said the possibility of bigger television deals for the smaller conferences could make it appealing.
"You make your own rules at that point," Jones told WDAE. "Football is the No. 1 sport on television right now and the advertisers want live programming. They don't want Hollywood shows because you can TiVo out the commercials. Live programming is a hot topic right now and I think there's a market for bigger numbers for the non-BCS teams."
Jones, who coached in the USFL from 1984-85 before the league folded, said if some radical changes aren't made, he believes some non-Power Five schools financially won't be able to compete and will "start dropping football."
Non-Power 5 Leaders Fight Back
ESPN college football reporter Brett McMurphy discusses the comments made by SMU coach June Jones regarding non-Power Five conference schools playing in the spring.