A statement from the Summers family through the Vanderbilt University Medical Center says Wesley, Jared and Branson remain in hospital care. They are asking for prayers that their parents, Jon and Janet, are found.
Officials have said at least seven people died in the wildfires but they have not positively identified any of the dead.
According to media reports, the family was vacationing in Gatlinburg and was separated while fleeing the fiery scene.
The statement says one of the sons talked briefly to share his feelings and concerns for his brothers and parents.
The statement says the brothers are so grateful for the outpouring of love and support by so many people.
A fundraising page has been set up for the care of three brothers.