Shares of General Motors (GM) - Get Report were higher by 2.42% to $35.56 on Tuesday morning, following a Wall Street Journal report noting that investor David Einhorn is pushing the auto company to split its common stock into two classes.

One class will pay dividends and the other would entitle holders to all earnings, including stock buybacks once the dividend is paid.

Einhorn's Greenlight Capital believes the split will attract new investors that would be willing to pay more for potential earnings growth which could boost the company's market cap by as much as $38 billion, sources told the Journal.

However, General Motors and Einhorn had been talking for about seven months, but GM is said to have "made it clear" to Greenlight Capital that it is not interested in pursuing a dual share class proposal, CNBC reports.

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GM believes the proposal creates risks that are "unacceptable" and calls the plan "unprecedented and untested," a spokesperson told the Journal

This story was updated from 10.53 a.m. EDT to include a CNBCreport and GM's comments to the Journal.