The X Factor semi-finalists said they could rival One Direction once the show comes to an end next week.
Jaymi Hensley told The Mirror: "We don't want there to be any limits on how big we can be.
"We would love to be as big as they are right now and break America and tour the world. Louis Walsh thinks the sky is the limit.
"We will have such amazing lives if we do well and we will be able to live a life that people dream of."
Josh Cuthbert added: "We want to do better than One Direction. They finished third and we want to finish first or second. It would be amazing to do that."
One Direction went on to find huge worldwide success after finishing third in the UK X Factor in 2010.
Union J will discover whether they have made the grand final in tonight's results show (December 2) at 8pm on ITV1.
The boyband recently told Digital Spy that they used to be the "weakest" singers in the competition.
Watch the group talk to Digital Spy below: