Campbell said in a statement Thursday afternoon its board of directors "remains dedicated to delivering a go-forward strategy that will drive value for all shareholders." It said it looks "forward to sharing the details of our plans when the company reports its fourth-quarter and full-year results on August 30 and engaging with our shareholders on our strategic plan."

In a separate filing by Strawbridge, meantime, he writes, "unless the Board's strategic review results in a new direction ... the only reasonable approach is to reconstitute the Board."

Loeb said he has had discussions with Campbell's interim CEO, Keith R. McLoughlin, and that the possibility of a sale is being evaluated as part of the company's ongoing strategic review. "The only justifiable outcome of the strategic review is for the Issuer to be sold to a strategic buyer," the filing said.

The hedge fund recently acquired a 5.65 percent stake in Campbell, according to a securities filing. The activist is planning to team up with shareholder George Strawbridge, a family member of the founder, to call for the sale, the filing said.

Third Point's Dan Loeb will call for the sale of Campbell Soup.

Campbell closed up less than 1 percent on Thursday. The shares have fallen 13 percent this year.

The 149-year-old soup company is viewed as vulnerable as it faces pressure on multiple fronts, following the unexpected departure of its CEO Denise Morrison in May.

Its wet soup business declined 1.9 percent over the past year, it told analysts in May. Its fresh food business, which includes Bolthouse Farms, is clocking a loss of roughly $50 million in earnings before interest tax depreciation and amortization, down from a $150 million gain, sources have told CNBC. Meantime, industry experts say, integrating its $6.1 billion acquisition of pretzel company Snyders-Lance will be difficult.

Loeb said he built the bulk of stake in the soup company following Morrison's exit.

For Third Point to agitate for a sale, it would need to win over enough support from the family. The descendants of John P. Dorrance — the man many say invented condensed soup — have multiplied across many different clans over the years, and they aren't all in agreement over whether to sell, sources have told CNBC.

Mary Alice Dorrance Malone is Campbell's largest shareholder, with a 17.7 percent stake in the company. Her brother, Bennett Dorrance, has a 15.4 percent stake. Other descendants hold a combined 7.9 percent of the company in the Campbell Soup voting trust. The voting trust decreased its position in Campbell in June 2017, according to Factset.

Whether the family can be pressured to sell is open for question. They've resisted selling in the past. And whether Campbell with attract a decent bid is also up for debate. The brand that became synonymous with American industrial success is no longer the prize for potential bidders it once was.

Loeb, though, in his letter writes that he is "aware that members of Issuer's founder's family hold a significant percentage of the voting stock in the Issuer but remind[s] the Board that directors bear fiduciary responsibility to all shareholders."

The soup giant is already working with investment bank Centerview Partners on the review. Centerview's co-founder, Blair Effron, has a close relationship with the soup company that dates back decades.