Magna International is among those interested in Chrysler
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Unions have urged DaimlerChrysler not to sell its struggling North American Chrysler business.
The president of the United Auto Workers (UAW) said he would press the firm to hold onto the business despite the heavy losses it has made recently.
With contract talks due to begin in the summer, the unions could potentially delay or complicate any sale.
Several potential suitors, including businessmen Kirk Kerkorian, are lining up bids for Chrysler.
'Status quo'
But analysts believe they are only prepared to pay a fraction of the $40bn which Mercedes-Benz paid for the business in 1998.
UAW president Ron Gettelfinger said he believed it was still "an option" for DaimlerChrysler to retain the business.
"I am going to continue to make the case," he said. "I believe we are better off where we are."
DaimlerChrysler revealed in February it was looking at Chrysler's future, with a disposal of the business a distinct possibility.
The firm made a $1.6bn loss last year and is looking to cut 13,000 jobs in order to make itself more competitive.
Chrysler boss Tom LaSorda did not comment directly on the union position but confirmed that "discussions continued" with potential buyers.
Last week Canada's Magna International confirmed it was considering making a bid for the up-for-sale carmaker.