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.



(Read more:Did investors miss the message on the value of Blackberry's BBM?)

Chen stressed that BBM's value came from its high level of engagement with enterprises and professionals. The company has launched its Enterprise Suite for BBM (eBBMSuite) - 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.