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.