Pfizer's animal health unit may be worth $20 billion--courtesy of Pfizer

Pfizer's animal health unit may be worth $20 billion, and that is the conundrum.

With the value having inflated beyond the reach of potential buyers, Pfizer ( $PFE ) has decided it must move forward with an public stock offering instead of a sale, perhaps as early as next month, sources tell The Wall Street Journal .

The drugmaking behemoth has decided an IPO of about 20% of Zoetis could bring roughly $4 billion and is the best way to get the most value out the unit, The Wall Street Journal says. The unit earned about $3.1 billion in the first 9 months of 2012. Pfizer will eventually spin off the remaining 80% tax-free to shareholders.

The company last year decided to unload the division as part of its plan to help replace revenue lost when its cholesterol-lowering Lipitor , the world's best-selling drug, was hit by generic competition. There had been rumors that Bayer or Novartis ( $NVS ) might be interested in buying it but those have cooled more recently.

Germany's Bayer in September did agree to pick up the much smaller animal health unit of Teva Pharmaceutical Industries ( $TEVA ) for $145 million. That was announced a couple of days after up-and-coming generic drugmaker Perrigo ( $PRGO ) announced that it was buying Sergeant's Pet Care Products for $285 million.