The paper said last week that Post is the third largest cereals business in the US by sales, after Kellogg and General Mills.
The Post product range includes Shredded Wheat, Raisin Bran, and Alpha-Bits.
Kraft formed part of the voluntary group of manufacturers, including Cadbury, Coca-Cola and General Mills, who collaborated over new reforms last month in an effort to preempt regulatory action.
The company claimed to be the first to use nutritional standards when advertising to children following pioneering the self-regulatory programme in 2005.
"Kraft advertises only better-for-you Sensible Solution products that meet specific nutrition criteria to children ages 6 - 11 years old, and we don't advertise to children under six," the company said in July.
This, according to the Wall Street Journal, has put pressure upon Post's product marketing and has affected sales.
The paper also claims rising prices for raw materials such as cereals and strong competition has also put pressure upon the cereal business.
"As a result of our investments in growth and our expectations for significant increases in input costs, particularly dairy, our profit margins will show further decline in the second half of the year," said Kraft's chief executive officer Irene Rosenfeld earlier this month.
The company's operating margins decreased to 14.5 per cent in the second quarter 2007 compared to 16.6 per cent in the second quarter in 2006.
Operating income declined 2.8 per cent within the North America snacks and cereals segment during this period, with sales of $1.6bn (€1.2bn).
The article claims PepsiCo, General Mills, and Ralcop Holdings are all logical buyers for the business although representatives from none of the companies were available for comment.