The Hopkinton, Massachusetts- based company has contacted firms including Oracle Corp, Cisco Systems Inc and Hewlett-Packard Co about selling itself, said sources who asked not to be identified.
EMC has also discussed a deal for its storage business with Dell Inc, they said.
No deal is imminent and a sale or spinoff may not result, the sources said.
EMC began holding a strategic review in the spring as Tucci, who has been CEO since 2001, is set to step down from that role some time before February, according to the terms of his employment agreement.
More recently, the company has faced pressure from activist investor Elliott Management Corp, which has amassed a stake of more than $1bn in EMC.
Elliott is pushing EMC to sell itself or spin-off software maker VMware, where it is the majority owner.
Dave Farmer, a spokesman for EMC, declined to comment, as did Kate Holderness, a spokeswoman for Hewlett-Packard; Deborah Hellinger, a spokeswoman for Oracle; and David Frink, a spokesman for Dell.
John Earnhardt, a spokesman for Cisco, didn’t immediately respond to a call for comment.
EMC’s talks with Hewlett-Packard and Dell were reported earlier by the Wall Street Journal.
Acquisition discussions between EMC and Hewlett-Packard were advanced and included a decision to have Hewlett-Packard chief Meg Whitman serve as CEO and Tucci as chairman, but there were disagreements over price and the next layer of management, said one of the people.
An outright sale of VMware would probably trigger a tax bill, making a spin-off a more attractive option, said one of the people familiar with the process.