Tyson, the largest U.S. meat processor, last week said it would buy Hillshire for $63 per share, valuing the company at $8.55 billion.
Hillshire said it does not have the right to terminate the merger agreement with Pinnacle Foods on the basis of the Tyson Foods offer.
Hillshire expects to hold its stockholder meeting as early as August.
The company will have the right to end the Pinnacle merger on Dec. 12 regardless of whether a shareholder vote takes place.
If Pinnacle Foods terminates the deal before Hillshire stockholders vote, Pinnacle may be entitled to a termination fee of $163 million.