At $40 per share, the value of the cash and stock deal would be worth $51.1bn.
Led by company co-founder and board member Jerry Yang, Yahoo now will be under pressure to lay out a strategy that will prevent its stock price from collapsing again.
Yang and the rest of the management team must convince Wall Street that they can boost Yahoo's market value beyond Microsoft's offer.
Yahoo's shares traded at $31 as recently as November, but have eroded steadily amid concerns about the slowing economy and frustration with the slow pace of a turnaround that Yang promised last June when he replaced Terry Semel as chief executive officer.
If successful, a merger of Microsoft and Yahoo would be the world's largest of two computer technology companies and create a formidable rival to internet search and advertising leader Google.
Yahoo has been considering options, including negotiating a higher price and striking a deal with Google to take over its search operations to keep Yahoo independent, the Journal said.
The newspaper reported Yahoo's board met on Friday.