The talks continued into Sunday night, the WSJ says, "as people involved in the negotiations aimed to finalize a deal within days."
The Journal reports that the deal will be led by company founder Michael Dell, along with Microsoft and Silver Lake Partners. The story says four investment banks are lined up to raise about $15 billion in debt to help fund the deal.
Dell is the world's third-largest PC maker, following only Hewlett-Packard and Lenovo.
Dell this morning is up a penny at $13.64.