According to the paper, the deal could be worth as much as $8.5bn (£5.2bn), which would make it Microsoft’s largest acquisition.
Both Microsoft and Skype have declined to comment on the story.
Luxembourg-based Skype has 663 million global users. In August last year it announced plans for a share flotation, but this was subsequently put on hold.
Internet auction house eBay bought Skype for $2.6bn in 2006, before selling 70% of it in 2009 for $2bn.
Skype is now majority-owned by a group of investors, led by private equity firms Silver Lake and Andreessen Horowitz.