The event is due to be the main qualifier for the 2016 Olympics in Rio de Janeiro and has also attracted interest from Glasgow and Paris.
The International Gymnastics Federation (FIG) are to make a decision at its Council meeting in San Jose on May 21.
USA Gymnastics have targetted the 2015 event because they believe it will attract the most interest in the United States.
"There's so much going on in the sports world in the United States on an ongoing basis that you want to bring the highest level of attention to an event like this. Doing it in the year before an Olympics allows us to do that," Steve Penny, the President of USA Gymnastics, told the Associated Press.
"This has the prestige, the magnitude that you want of being a full-team event, a qualifier for the Olympic Games.
"It's also, from a business standpoint, at a time we think can get people's attention."
If successful it would be the fourth time that the US has hosted the event, having previously staged them at Fort Worth in 1979, Indianapolis in 1991 and Anaheim in 2003.
"It really does give your country a boost," Penny said.
"Hosting a World Championships means giving more athletes, more fans, an opportunity to touch the sport at the highest level.
"There's just a tremendous intrinsic value to having a world championships in the U.S. that goes beyond dollars and cents."
October 2010: Glasgow launch bid for 2015 World Gymnastics Championships