Activist investor Daniel Loeb's hedge fund Third Point is looking to replace Campbell Soup's entire board, The Wall Street Journal reported Thursday, citing people familiar with the matter.

Such a campaign would shine an unprecedented spotlight on the three descendants of Campbell's founder who sit on the soup company's board. Two of those descendants, Bennett Dorrance and Mary Alice Dorrance Malone, together hold a 33 percent stake in Campbell. The fiercely private siblings, whose father served as Campbell chairman, have resisted past pressure to sell the company.

The third family member on the board is Archie Van Buren, nephew to Bennett and Mary Alice. Van Buren is a trustee in the Campbell Voting Trust, through which other descendants together hold a combined 7.9 percent stake in the company.

Campbell requires two-thirds shareholder vote approval for a deal.

The company announced last week it is selling its international and fresh food businesses, as the 149-year-old condensed-soup maker struggles to regain its financial footing and refocus on its signature packaged foods. The announcement came after a three-month critical review, propelled by disappointing earnings and the surprise departure of Campbell's CEO.

Last week's announcement, though, was underwhelming to Third Point, the Journal reported. The hedge fund believes a fresh slate of directors would put all options for Campbell back on the table.