It's unclear if this would be a full merger, or if Dell would just buy parts of EMC's business. Either way, it would be a huge deal between two of tech's biggest companies.
EMC makes software and hardware for high-efficency data centers. It's the parent company of the successful VMware.
Meanwhile, PC and server manufacturer Dell delisted itself from the public markets in 2013.
Analysts have been calling for Dell to acquire EMC's data business, but it could end up taking over the entire company.
Shares in EMC are up over 9.4% in after-hours trading. The Journal's report indicates that general market voltatility could slow down this deal, if one were to be reached.