Tyson said it would offer $50 per share, representing a premium of about 11 percent to Hillshire's closing on Wednesday.
Shares of Hillshire, the maker of Hillshire lunch meats and Jimmy Dean Sausages, were trading above Tyson's offer at $51.70 before the bell on Thursday. Tyson shares were up 4 percent.
The offer comes two days after Pilgrim's Pride offered to buy Hillshire in an all-cash deal valued at $6.4 billion to expand its protein footprint with Hillshire's sausages and lunch meats.
Hillshire also offered this month to buy Pinnacle Foods, known for its Birds Eye frozen vegetables, in a $4.3 billion deal.
Tyson said on Thursday its offer for Hillshire would stand only if the Pinnacle deal was terminated.
Tyson said it had secured financing from Morgan Stanley Senior Funding.
The company said it expected the proposed to deal to add to its earnings per share in the first year after completion.
Tyson shares closed at $40.75 on the New York Stock Exchange on Wednesday. (Click here for the latest quote.) Hillshire shares closed at $44.99 on the New York Stock Exchange on Wednesday. (Click here for the latest quote.)