You may soon be seeing and sharing advertisements during your Skype calls, if the company's new CEO has his way.

Speaking at the Fortune Brainstorm Tech conference in Aspen, Tony Bates discussed ways he might monetize the popular Internet phone service, once its $8.5 billion acquisition by Microsoft is completed.

"Obviously, there's a very rich long-term advertising play," Bates said. "The one I want to tease right now is in-call advertising. The average length of a video call is going up — it's about 27 minutes now — and you're doing a lot of things in that time. If we're talking, you're not just looking at me, so we have a lot of opportunities there."

Asked if that might involve ordering a pizza, for example, Bates responded: "Why not? Why not, because we have this intimate relationship, at the end of the call, I share an ad with you? Watch this space. We think this is going to be a very exciting area."

Bates, a former executive at Cisco, was tapped as Skype CEO back in October. After the Microsoft acquisition, he says, he is committed to staying in charge of Skype, which will be run as a separate division — an unprecedented level of independence for a company snapped up by the software giant.

In March, the company began rolling out advertising from major sponsors on its homepage. Bates didn't say whether in-call ads would appear as pop-ups, audio ads or some other form, but it seems Skype is considering all its options.