Dell Inc. is offering about $33 a share to acquire EMC Corp., a person with knowledge of the matter said, in a deal that would create a corporate-computing colossus and help both companies cope with a demand slowdown.

The proposal includes a tracking stock in VMware Inc. valued at about $8 a share that would be issued to EMC shareholders, said the person, who asked not to be identified discussing private matters. A deal may be announced as soon as Monday, the person said. Dell is speaking to banks about raising at least $40 billion to finance the purchase, a person with knowledge of the matter has said.

“This is a very good offer and much closer to what EMC shareholders were hoping for,” said Daniel Ives, an analyst at FBR Capital Markets & Co. “This would be viewed as a solid way to end a bad situation after years of struggles.”

A deal would bring together the largest storage maker and the No. 2 server company as the industry undergoes rapid change with the shift to mobile and cloud computing. Dell, which was taken private for about $25 billion in 2013, will use the combination to expand its product lineup in high-end data storage equipment and seek to lure customers away from Hewlett-Packard Co. and other rivals. VMware, which makes tools that help servers run software more efficiently, is valued at $32.3 billion, while EMC has a market capitalization of $53.6 billion.

EMC Resolution

For EMC, the agreement resolves a long overdue leadership succession and a standoff with activist investors. EMC, which has been publicly traded since 1988, had been looking at strategic options for boosting its share price, while activist investor Elliott Management Corp.had pushed for EMC to sell itself or spin off VMware. EMC Chief Executive Officer Joe Tucci had delayed his planned retirement amid the wrangling. The current plan would have Michael Dell run the combined entity, a person with knowledge of the matter has said. David Frink, a spokesman for Dell, and Dave Farmer, a spokesman for EMC, declined to comment. It’s a risky bet. The prevailing trend in technology is to separate and focus on fewer businesses to compete against nimbler competitors. Hewlett-Packard is splitting in two next month, a step that EBay Inc. took earlier this year.