The report cites two unnamed sources, including one person who said IBM has informally approached RIM about buying the unit. The unit is valued at at around $2 billion, industry experts say.
Officials from IBM and RIM declined to comment on the report.
However, one person with knowledge of the situation told Computerworld that the report "not true" and that IBM is interested in buying RIM's crown jewel.
The RIM unit includes BlackBerry Enterprise Server (BES) support and related software functions. The deal could also include RIM's network operations center (NOC).
That operation also supports servers used to provide secure Internet connections for millions of RIM users. Many of those users work at large banks and financial services firms that have come to rely on BES for high-level security in email transmissions from and to mobile devices.
RIM says that about 250,000 BES servers, and about 78 million BlackBerry devices, are used at workplaces around the world.
The enterprise services business is widely considered RIM's crown jewel, even as the former smartphone leader has struggled since the introduction of the iPhone five years ago to produce smartphones attractive to consumers.
The unveiling of smartphones running RIM's BlackBerry 10 operating system have been delayed over the past year and are expected to launch early in 2013.
RIM CEO Thorsten Heins has in recent weeks been conducting a strategic review at RIM amid layoffs of about one-third of the company's work force.
Heins has said that RIM may license the BlackBerry OS to third parties, but has not specifically talked of selling off the enterprise business unit or the NOC.
RIM's NOC transmits all BlackBerry data for both enterprises and consumers.
Any deal to buy RIM's enterprises services businesses would have to include an agreement on whether RIM would retain control over part or all of the NOC, including consumer-related traffic, analysts said.
Ken Dulaney, an analyst at Gartner, said an IBM acquisition of RIM's enterprise unit "would make a lot of sense to me. Customers would love knowing that an IBM is behind this."
Still, he said RIM probably wouldn't sell the unit, considering that the company has some $2.2 billion in cash and no debt, and wouldn't want to give up such a vital asset.
"RIM might give up just the NOC and keep the BES servers that go on-premise with customers," Dulaney added.
Jack Gold, an analyst at J. Gold Associates, said the enterprise services business is "very profitable for RIM, so why would they want to sell it?"
Still, Gold said IBM would like RIM's software technology, to add into its own WebSphere software and perhaps even into Notes. "IBM is behind on mobile and this software would give them a boost," he said.
Both Dulaney and Gold had cast doubt on a Jefferies financial analyst's report this week that said Samsung has considered buying RIM or licensing its BB10 OS.
Heins is expected to update investors on the RIM strategic review at the next earnings call on Sept. 27.