The band, who were runners-up in the final, are angry that their contract stipulates that they have to be looked after by Modest Management.
All finalists have to sign the controversial contract that binds them to the management company for a minimum of three months after the show finishes.
"JLS are so popular - they could be the new Blue with a sexier, cooler edge to them," a source told The Sun.
"They need to be managed by someone who cares about them and Louis really does.
"The boys are really desperate to go with Louis and he just wants to get them signed up and recording. But at the moment, Modest are refusing to let them go."
Mentor Walsh recently claimed that the band had the potential to match the success of Westlife.