NEW YORK - A number of private equity firms put in second round bids for Dow Chemical's Styron unit a week ago, including buyout firms TPG and Apollo, several sources said.

Dow, the largest U.S. chemical company, put Styron up for sale in July and said at the time the unit could fetch $1 billion to $2 billion. Dow has said that it hopes to sell the unit, which makes polystyrene, rubber and latex, by the end of the first quarter of 2010.

Other private equity bidders for the unit include Bain Capital, the sources said, but it remains unclear how many of the firms are still in the process.

The sources, familiar with the matter, declined to be identified because the process is not public.

All the private equity firms declined comment. Dow did not immediately respond for comment. (Reporting by Megan Davis; editing by Carol Bishopric) (Additional reporting by Ernest Scheyder and Matt Daily)