The German automotive supplier is in talks with five investors that are prepared to pay a higher price than Schaeffler.
Sources have said one of the investors was the Japanese tyremaker Bridgestone, reported the Financial Times.
But bankers said the offer was not a realistic option for Conti as it would probably involve a break-up of the company.
To earn more time for a possible deal, Conti is considering holding an extraordinary shareholders’ meeting.
This would automatically extend Schaeffler’s offer, due to end on August 27, by six more weeks.