Carlyle and Apollo were thought to be teaming up for a joint $4bn bid for the business, but both have made individual bids with the latter unwilling to increase its offer, according to Reuters.
The manufacturer rejected a string of bids from private equity firms in April, with TPG and Advent joining up for a deal as well as CVC Capital and Clayton Dubilier and Rice.
Blackstone and Bain also paired up in an attempt to buy the business, as did KKR and Onex, it is believed.
Despite the interest many of the firms are thought to have had misgivings about the earnings assumptions DuPont had made for its business, as well as a general decline in demand for car paint from body shops.
The latest Reuters report suggested Carlyle had made the highest bid in an auction which could go as high as $4.5bn.
DuPont, which has been developing, producing and marketing car coating systems for more than a century, has key customers in Maaco, Ford and General Motors.
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