A bag of Tyson Foods Inc. frozen chicken is arranged for a photograph in Tiskilwa, Illinois, U.S., on Thursday, May 5, 2016. Tyson is scheduled to release earnings figured on May 9.

Meat processor Tyson Foods has held talks about buying privately owned California-based Foster Farms for roughly $2 billion, people familiar with the situation tell CNBC.

The two sides are disagreeing over price, said these people, and it is possible the talks fall apart. If a deal is consummated, it is still at least several weeks away.

Shares of Tyson briefly dropped nearly 2 percent on news of the talks, but quickly rebounded to $61.64 a share, off less than 1 percent.

Tyson, one of the biggest food companies in the U.S. by sales, supplies meat to restaurants and other food-service customers. It also sells branded chicken, beef and pork under labels such as Jimmy Dean, Hillshire Farm and Golden Island Jerky.

The deal talks come just months after Tyson closed its $2.16 billion acquisition of McDonald's meat supplier Keystone Foods, which further expanded its capabilities in Asia.

An acquisition of a U.S. brand such as Foster Farms, which makes branded chicken, turkey and frozen foods, would therefore mark a mild change in course for Tyson. It would instead echo a strategy it pursued in 2014, with its $7.7 billion acquisition of Hillshire Brands, which brought with it Jimmy Dean sausages and Ball Park hot dogs.

Tyson executives were asked about their global M&A strategy during the company's November earnings call. Of particular concern to one analyst was international expansion in the context of geopolitical uncertainty and currency fluctuations.

In response, CEO Noel White said, "We're forecasting about 90% of the growth in global protein demand will take place outside the United States. We do plan to participate in that demand growth. ... My priority is no different than ... my predecessors [which have been] ... to grow our business in prepared foods, value-added products and in the international market, simultaneously working to provide stability with more of the commodity portions of our business."

White took over as CEO on Sept. 30, 2018, after serving as Tyson's group president of beef, pork and international.

Foster Farms was founded in 1939 by Max and Verda Foster. It owns farms in California and Louisiana and also works with 30 family-owned farms in Washington and Oregon. In 2016, it named Laura Flanagan its CEO, taking over for Ron Foster, grandson of the company's founder.

Tyson, founded in 1935 by John W. Tyson, generated about $40 billion in sales last fiscal year. Shares of the company, which has a market capitalization of $18 billion, are down 15 percent over the past year.

The people requested anonymity because the talks are confidential. Tyson said it does not comment on rumors or speculation.

A spokesperson for Foster Farms told CNBC that, as a policy, it "never comments on speculated mergers and acquisitions activity."

The spokesperson added that, "While inquiries and rumors have come and gone for decades, Foster Farms has thrived as a family-owned company for 80 years. We are fully confident in our future success as a stand-alone company."

— CNBC's David Faber contributed reporting