John Chen's comments come a week after Facebook bought WhatsApp, a messaging application for smartphones, for up to $19 billion.
(Read more: Zuckerberg says WhatsApp worth more than $19B )
With regards to BBM - which has around 85 million active users, compared to WhatsApp's 450 million-plus - Chen said: "I work for the shareholder. Standard answer. If somebody comes to me with $19 billion, I would definitely sell it. I would recommend to the board to take it."
Chen added, however, that he did not look at BBM in that way.
"I know there's a lot of value in messaging businesses... I think the right thing to do is to expand that and market as big as possible and then I (will) worry about the valuation later," he said.
Chen stressed that BBM's value came from its high level of engagement with enterprises and professionals. The company has launched BBM Enterprise Suite (eSuite) - a range of products and services designed to make BlackBerry's messaging service more friendly to enterprises - which it argues provides the most secure and reliable real-time mobile messaging in the industry.
(Read more: BlackBerry bets on BBM with Windows, Nokia deal )
There is a renewed focus on BBM at BlackBerry, which on Monday announced that the messaging service would be available to Microsoft Corp's Windows Phone and the upcoming Nokia X platforms in the coming months.
It comes as BlackBerry continues to battle with the likes of Samsung and Apple for smartphone market share. Last year, Android and Apple's iOS accounted for 93.8 percent of all smartphone shipments - up from 87.7 percent in 2012 - as BlackBerry's share fell 40.9 percent, according to data from the International Data Corporation (IDC).
Late Monday, BlackBerry confirmed that its Head of Design Don Lindsay - a long-time Apple and Microsoft designer instrumental in the design of the BlackBerry 10 - had left the company. It is the latest in a string of departures under Chen, after the executive in charge of BBM left earlier this month and the head of global M&A departed in December.
At the Mobile World Congress in Barcelona, BlackBerry also announced that Daimler AG and Airbus Group were among the latest multinationals to adopt BlackBerry products. This is a welcome announcement for the smartphone maker after recent disappointments in its relationship with the U.S. Army.
Towards the end of last year, the U.S. Army - which has about 100,000 government-issued phones, around 70,000 of which are BlackBerrys - announced that while it was moving to the new BlackBerry 10, it was also launching an 18-month pilot program with Android and iOS phones.
(Read more: BlackBerry to be profitable by 2016: CEO Chen )
Chen said it was unfortunate this had happened, but added: "I think we've kind of made up a little bit already."
"But I'm going to stand my ground. Obviously, I feel very strongly about our device, so anybody who wants to intrude into our space, we have a very loyal customer base. You can rest assured that BlackBerry is not going to back down."
-By CNBC's Kiran Moodley. Follow him on Twitter @kirancmoodley
image: © overthinkingme