An estimated 10,000 to 20,000 jobs will be axed, Sky News said, citing unidentified sources. The number has not yet been finalized and Gulliver will lay out the plans at an investor presentation on June 9, the broadcaster said.
It was unclear how many of those cuts would come from moves already announced by the lender.
HSBC's shares fell 0.5 percent in Hong Kong on Tuesday morning, underperforming the Hang Seng Index.
HSBC declined to comment on the Sky report.
Low interest rates and tougher regulations have hurt HSBC more than most other banks in recent years, meaning Gulliver has missed some of his profit and cost targets.
In response, he has sold or exited 77 business units since