In 2006, Gibb bought the lakeside residence in Hendersonville, Tenn., where Cash and wife June Carter Cash lived for nearly 40 years. The home was undergoing renovations when it was destroyed by fire April 10.
Gibb said he would rebuild on higher ground surrounding the site of the gutted house, preserving the "sacred" original foundation to honor the iconic music couple who made their home there, E! News said.
"To the Cash Carter families we owe the highest respect and the deepest regret that our dream could not be realized," Gibb and his wife, Linda, said in a statement, referring to their plan to remodel the house.
"Now there is a new dream for us and a new beginning."
Fire officials ruled the blaze was an accident, saying flammable materials likely were sparked by a piece of electrical equipment.