Symantec Corp. has received interest from a pair of private-equity suitors seeking to buy the cybersecurity firm for more than $16 billion after it agreed to a sale of a big chunk of its business, according to people familiar with the matter.

Permira and Advent International Corp. recently approached Symantec proposing a takeover deal valuing Symantec at $26 to $27 a share that would hand them the company’s consumer operation while preserving the sale of its enterprise business to Broadcom Inc. Such a structure could reduce...