The two bidders are competing for Opel, in which GM is relinquishing control in return for state support for the local carmaker which it needed after filing for bankruptcy protection in June.
GM's new board meets later on Monday and industry sources have said Opel will likely be discussed.
German Economy Minister Karl-Theodor zu Guttenberg said in a weekend newspaper interview the two suitors must improve their bids to win government backing.
Magna wants to expand Opel's full-scale car assembly business and forecasts high growth rates, particularly in Russia, home of its bidding partner, Sberbank <SBER03.MM>.
RHJ aims to shrink production to return Opel to profit and may be open to selling it back to GM at a later date.
In a blog entry posted on the GM Europe's website last Tuesday, chief negotiator John Smith said he still expected a deal to close by the end of September, although no preference had been made yet for one of the two bidders, and key points with Magna's offer still had to be resolved.
The German states that are home to Opel plants and the federal government have expressed a preference for Magna's bid.
(Reporting by Gernot Heller, writing by Paul Carrel)
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