The layoffs will be across the board and likely occur in waves, the newspaper reported.
BlackBerry, which once dominated the corporate smartphone arena, last month said it was considered an outright sale of the company as it reviews its options. It has struggled in recent years to stanch rapid market share losses to rivals like Apple Inc and Samsung Electronics Co Ltd.
BlackBerry, which has already laid off hundreds of employees this year and previously warned that further job cuts were in the offing, declined to comment on the report or the magnitude of the reported layoffs. It employed 12,700 people as of March.
"We will not comment on rumors and speculation," BlackBerry spokesman Adam Emery said.
"We are in the second phase of our transformation plan. Organizational moves will continue to occur to ensure we have the right people in the right roles to drive new opportunities."
The report comes the same day the Canadian company introduced the Z30, a top-of-the-line smartphone intended to help the former industry pioneer wrestle its way back into the intensely competitive smartphone market.
But investors have grown increasingly nervous about BlackBerry's future as its market position crumbles. The company has been facing persistently lackluster sales of devices that run on the BlackBerry 10 operating system.
Shares in the company slid 1.5 per cent in Toronto to 10.72 Canadian dollar apiece, and fell almost 1 per cent to $10.45 on the Nasdaq in the afternoon.
Copyright @ Thomson Reuters 2013