Shuanghui, which is China's biggest pork producer, is offering to pay for the company in cash.
The deal, if approved, will be the largest takeover of a US company by a Chinese rival.
In recent years there has been an increased appetite among Chinese firms for acquisitions abroad.
In the US, however, regulators have blocked a number of potential purchases on national security concerns.
Smithfield, which owns the Armour and Healthy Ones brands, said the deal would allow the firm to expand the sale of of its brands abroad.
However, the takeover bid is likely to be closely scrutinised in the US by regulators due to a regular series of Chinese food scandals, including the sale of tainted meat.
In 2011, China's state broadcaster CCTV revealed that Hong Kong-based Shuanghui's pork products contained the banned chemical clenbuterol, which makes the meat leaner.
One of the most infamous foods scandals was in 2008, when six infants died and about 300,000 fell ill from tainted milk powder. It was later found to have contained melamine, an industrial chemical.
As a result, there is increasing demand among Chinese consumers for foreign food brands, which are viewed as a safer alternative to local products.