Selling Smithfield Foods in parts could bring more value to shareholders than the $4.7 billion takeover of the entire Virginia-based company by a Chinese meat producer, Jeffrey Smith, CEO of activist hedge fund Starboard Value, told CNBC on Monday.

"We identified—and had conversations with some, and we believe there are many others—that are interested in pieces of the company for what would add up to more value than the whole," Smith said in a "Squawk Box" interview.