Larry Ellison, founder and chief executive of Oracle Corp., may be entering the end game in his four-year play to consolidate the business-software industry around his company.

The software giant disclosed a $6.7 billion unsolicited offer to buy BEA Systems Inc., a Silicon Valley company that helped build the market for Web-services software. The bid, a 25% premium to BEA's closing price Thursday, comes as activist investor Carl Icahn, BEA's biggest shareholder, has put pressure on the smaller software company to sell itself.