Other interested bidders include US private equity firms Advent International and TPG Capital, said the sources, all of whom declined to be named as the details of a possible deal are not yet public.
Alliance Tire aimed to generate sales of more than $600 million in 2012, its website showed.
U.S.-based private equity firm Warburg Pincus, which invested in Alliance in 2007, is selling its roughly 72 percent stake in the company, the sources said, adding that final bids are expected to be invited by the end of this month.
Two other minority investors may also sell their stakes in Alliance, giving the buyer roughly 75 percent of the tyre maker, two of the sources told Reuters on Friday.
The company owns two manufacturing plants, one each in Israel and India, and has a sales presence in more than 120 countries, according to its website. Alliance's tires are also made at contract manufacturing facilities in China and Taiwan.
Ashok Mahansaria, founder of Alliance Tire Group, did not respond to an email seeking comment. Warburg Pincus and Temasek declined to comment when contacted by Reuters, while KKR, Advent and TPG did not immediately respond to requests for comment.
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