Pactiv has about $1.5 billion in debt and the Apollo deal would be among the largest leveraged buyouts in the past two years, according to the Journal.
The paper said any deal is a few weeks away and faces several hurdles. The Journal did not give the potential value of the deal.
Pactiv and Apollo could not be immediately reached for comment by Reuters outside regular U.S. business hours.
Pactiv shares fell 0.6 percent to $23.97 on Friday on the New York Stock Exchange, valuing the company at $3.2 billion, according to Reuters data.
In April, Pactiv said its first quarter profit fell 38 percent due to sluggish demand and high raw material costs and the company also trimmed its full-year forecast.
Demand for Pactiv’s products waned during the recession as consumers ate out less but there has been some improvement in recent months. (Reporting by Sakthi Prasad in Bangalore; Editing by Anshuman Daga)