The deal could be announced Monday, CNBC reported, citing a source close to the case.
According to the source, Microsoft made an initial offer in December and is willing to pay $56 per share for Nuance, which represents a premium of 23% compared to the group's closing stock price on Friday.
If the deal goes through, this would be the second-most important acquisition for Microsoft after its $27 billion purchase of LinkedIn in 2016.
Neither Microsoft nor Nuance responded to Agence France-Presse's (AFP) request for comment.
Nuance, which is based in Massachusetts, provided the speech recognition engine for Siri, Apple Inc.'s virtual assistant. Siri is an application that combines speech recognition with advanced natural-language processing.
The company works with organizations in health, financial services, telecommunications, government and retail.
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