The revised bid will allow Lyondell's creditors to opt for cash or equity as part of the deal, Bloomberg reported.
Reliance, India's largest-listed company, had previously offered a deal that valued Lyondell at $13.5 billion, a source told Reuters last month.
Lyondell recently settled a dispute with creditors that paved the way for an exit from bankruptcy, leading analysts to suggest that Reliance may be forced to raise its offer or abandon it.
Spokesmen for Reliance and Lyondell did not immediately respond to requests for comment on the Bloomberg report.
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