Starboard privately named its nominees in June after buying the stake worth about $670 million, the Journal said, citing sources.
According to Starboard, Symantec needs operational changes to improve margins, especially in its business-facing segment, the Journal said.
Starboard says its nominees could help improve operations as well as amend issues with financial reporting, and the suggested members include a former chairman of antivirus company AVG Technologies and a former Intuit executive, the Journal reported.
Symantec, which is in the midst of an internal accounting probe, saw its first-quarter revenue falling 1.6 percent, hurt by weaker demand from companies.
Starboard and Symantec were not immediately available for comment outside of regular business hours.