General Motors Corp. could face a proxy fight with billionaire investor Kirk Kerkorian after the ailing motor company rejected a possible alliance with Renault SA and Nissian Motor Co. that had been recommended by Kerkorian, Bloomberg News was reporting Monday.

The Oct. 6 departure of Kerkorian aide Jerome York from the GM board and a subsequent letter blasting GM’s board raises the prospect of a proxy contest, and puts more pressure on GM to go back to the table, Bloomberg said.

York resigned two days after GM announced the end of alliance talks with Nissan and Renault, and Kerkorian hinted in a filing Monday that York’s resignation signaled that he may not buy any more GM shares. There have been reports that the billionaire was considering upping his stake in GM to 12 percent.

Kerkorian is founder of Beverly Hills-based investment firm Tracinda Corporation and owns about 10 percent of GM’s stock. Shares in GM were up 26 cents to $31.31 in early trading Monday.