Chrysler (NYSE: DAI) joined Ford (NYSE: F) and General Motors (NYSE: GM) today when it proposed to divest its non-core assets. It is looking at divesting Chrysler Transport, which manages deliveries of supplies to Chrysler plants, and its Mopar unit, which makes high-performance and specialty auto parts, people familiar with the matter told the Wall Street Journal (subscription required).

Obviously, the United Auto Workers oppose the divestitures. It is unclear if the divestiture of the assets will be part of the final agreement between the UAW and the newly independent Chrysler.

In addition to the potential non-core asset sales, the company already has a restructuring plan that calls for 13,000 jobs cuts and a return to profitability next year.

The UAW's talks with Chrysler have also revolved around the auto maker receiving a concession on health care costs, similar to what Ford and GM received back in 2005. Chrysler also wants to outsource non-core employees to a third party, similar to the agreements Ford currently has with UAW locals at individual plants.

The UAW now faces a battle at each of the three major Detroit automakers. The contract between the UAW and Chrysler expires on September 14.