SAN FRANCISCO — Dell Inc. is in advanced talks to buy EMC, people briefed on the matter said on Wednesday, potentially uniting two stalwarts of the technology industry as each faces pressure to revive its business prospects.

A deal would involve mostly cash, some of these people said. An agreement could be reached within a week, although these people also cautioned that talks were continuing and might still fall apart.

A takeover of EMC would answer years of questions about the fate of the 36-year-old company, which has grown from data storage into a collection of businesses, including network security and content management for corporate clients.

Critics have contended that EMC’s vaunted “federation” business model has produced little benefit for shareholders in recent years, with some investors calling for a breakup. Such demands have been largely rebuffed by EMC’s longtime chairman and chief executive, Joseph M. Tucci, who is 67.