A possible bankruptcy plan being discussed for General Motors includes quickly forming a new company of the automaker's most profitable parts, while a group of other units would remain under bankruptcy protection for a longer period, a source familiar with the plans told Reuters on Tuesday.

GM also would seek to have a new deal in place with the United Auto Workers union prior to any bankruptcy filing, the source said.

GM warned earlier on Tuesday that there is a rising chance it could file for bankruptcy by June, as the company has 60 days to reach deeper concessions with bondholders and unions after its previous restructuring plan was rejected by the U.S. government as insufficient.

While the automakers would still prefer to avoid bankruptcy, advisers to both GM and Chrysler LLC have been working to prepare for potential bankruptcy filings that would aim to preserve, or sell off, the best parts of the companies.

Under the plans being considered, GM would seek to quickly move its most profitable units into a new company separate from its other units in the early days of the bankruptcy filing, said the source who asked to remain anonymous because the person was not authorized to speak to the media.

The aim would be to show consumers, taxpayers, and the government that the new GM can survive and compete in the autos sector as a viable company, the source said.

Old components of the company not included in the new GM, such as Saturn and Hummer, would remain in bankruptcy over a longer period of time to be sold or wound down, said the source.

During a transition period, the new GM would have to coordinate with the old GM for some time and share certain operational activities, like accounting and insurance, the source said.

GM has recently made progress on its negotiations with the United Auto Workers, winning deep concessions on healthcare and entry-level wages, but negotiations are ongoing over the fate of its obligations to 775,000 retirees.

As part of the negotiations to reduce or eliminate certain retiree benefits, the union is likely to seek some compensation, which could include a stake in the new GM, cash from a sale of the new GM, or any other source of funds, the source said.

Bondholders, a key constituency in the GM restructuring have said they were braced for a reduced offer of pennies on the dollar for about $28 billion in GM debt.

(Reporting by Emily Chasan; additional reporting by Chelsea Emery and Tom Hals; editing by Carol Bishopric)