The subsidiary would be called BBM Inc, the newspaper said.
A BlackBerry spokeswoman told Reuters the company cannot comment on rumor and speculation.
Two sources familiar with the company's thinking, who declined to be named because they are not authorized to discuss the matter with the media, told Reuters the company has reallocated internal resources and personnel to work exclusively on fine-tuning the BlackBerry Messenger service ahead of its launch on competitors' devices.
However, there is no immediate plan to spin off the unit, one of the sources said, adding that BBM for Apple's iPhone and devices using Google's Android should be available to consumers in the next few weeks.
The instant messaging service has about 60 million users who send billions of messages a day. BlackBerry has sought to add value to the service, even as the popularity of the company's own handsets shrinks, by adding video calling over WiFi and working to make the service available to users of other devices.
The company has already announced plans for BBM Channels, which would allow advertisers to promote special deals or to target markets narrowly.
BlackBerry is also considering making BBM available for desktop computers, the Journal said, quoting a person it said was familiar with the matter.
BlackBerry said earlier this month it was looking into options for the company, which could include an outright sale.
BlackBerry's shares were 3 percent lower at C$10.63 on the Toronto Stock Exchange early on Tuesday afternoon. They have lost well over three-quarters of their value since a peak in early 2011, and are down more than 7 percent so far this year.
© Thomson Reuters 2013