The deal, first reported in the Wall Street Journal, could close as early as today and would rank as Microsoft's largest ever acquisition, after the $6bn it paid for online advertising company aQuantive in 2007.
Microsoft has traditionally favoured developing small start ups rather than major acquisitions, and gave up on a potentially disastrous $48bn offer for Yahoo nearly three years ago (Yahoo is now valued at around half that sum).
The acquisition of Skype would give Microsoft access to around 660 million users worldwide, providing a presence in the online voice and video communications market.
It is also thought that Microsoft could integrate Skype into its Xbox Live or Xbox Kinect systems, along with the flagship Office product range.
However, people close to the talks cautioned that the sale is not yet finalised and could still fall apart, with potential sticking points including Skype's long-term debt of around $686m.
The future of Skype has been a subject of great speculation over the last few months, with rumours of Facebook, Google and Cisco Systems all considering bids.
Online auction site eBay bought Skype for $2.6bn in 2005, but later wrote down the company's value by $1.4bn, before selling off a 70% stake in 2007 to technology investors.
Skype, which uses voice over Internet Protocol (VoIP) technology, has struggled to make a profit in the eight years since it was founded. Last year, the company posted revenue of $860 million, delivering $264m in operating profits, but still endured a loss of $7m.