Asik is a second year player, so he should be covered by the Gilbert Arenas provision and can't be offered a starting salary of more than the average salary. As a second-year, early Bird free agent, the Bulls could match an offer sheet (and I doubt the Bulls will let Asik be unrestricted by not giving him a qualifying offe) without having to use the MLE.
So, it basically sounds like Asik will be a Bull next season unless Chicago thinks he is not worth $5m/year or really, really wants to avoid the luxury tax even if it makes the team less of a contender.