Fortune Brands planning a breakup of the company, selected Morgan Stanley to run an auction for its golf division in a sale that may fetch as much as $1.5 billion, said people with knowledge of the matter.

Fortune announced Dec. 8 that it would split into three separate businesses and focus on distilled spirits, after activist investor William Ackman acquired a stake. The company will spin off its home and security division and sell or spin off the golf unit, which makes Titleist golf balls.

Several major private-equity firms are considering buying Fortune Brands’ home products unit, sources said.