Campbell Soup has begun the process of selling off a number of its brands, including its Arnott's cookie and crackers business, as it looks to pay down the debt left in the wake of its acquisition of Snyder's Lance earlier this year, people familiar with the matter tell CNBC.

The soup company had previously said it planned to sell its international and fresh food food businesses after a three-month review it announced after a string of poor quarterly results. It said focusing on its signature packaged food would help regain its financial footing. The decision came despite pressure from activist fund Third Point, which initially said the only justifiable outcome of the review was a sale to a strategic buyer. Third Point has since said it would also accept other moves for Campbell, including a breakup.

Campbell has sent out materials to tease the sale of its Australian Arnott's biscuits business and Kelsen baked snacks that could fetch $2.5 billion to $3 billion from buyers. The biscuit and cracker maker is the largest in Australia and has therefore caught the eye of a number food companies that are eyeing global expansion as challenged U.S. grocers continue to exert their pressure.

Food companies — including Oreo-owner Mondelez, Kraft Heinz and Ferrero, which owns Nutella — are among those eyeing the business, the people said.

Snacks have become increasingly important for food companies to buy as more and more people eat on-the-go and sales of grocery staples, like cereal, have slowed. In the U.S., though, there are few brands available to buy to move the needle for companies that generate billions in annual sales.

Arnott's gives buyers a chance to buy a large business in an established market. Still, with Australia relatively isolated, it would also likely require a buyer with an existing global footprint and may also limit their ability to expand the brand further into other international markets like China, say people familiar with the industry.

Campbell expects to sign non-disclosure agreements for its international snack business in the next weeks, and will then begin to send out confidential materials, the people said. This will launch a formal sale process. While such processes take weeks, it remains possible a keenly interested party could expedite it by lobbing in a particularly high bid, some of the people said.

One likely consideration in the sale process is potential anti-trust issues due to Arnott's hold on the Australian cookie market. Campbell is under pressure from activist investor Dan Loeb and his hedge fund Third Point, which have chastised it for poor performance, making it unlikely it will want to take on much risk that antitrust authorities could oppose a deal.