Bennett, who has been considering an online simulcast of one of the BBC's channels for the past few months, told BroadcastBBC2's loyal following would make it a good testing ground. "BBC2 is a home for passions. When people phone up to request programmes, it's not necessarily the high-profile programmes they go for. That makes me think BBC2 is a great thing for this," she said.
She added that the online version, which would be accessible before the launch of the BBC's MyBBCPlayer, could offer some of the channel's back catalogue.
The corporation is now looking into writing an online clause into BBC2's licence as part of the Charter review process.
It would be the first time a terrestrial channel has been streamed over the web, and would be a vital test for the MyBBCPlayer, which the BBC eventually wants to use to stream all its channels over the net.
Bennett's comments came in the wake of BBC2 controller Roly Keating's admission at Edinburgh that the channel had hit its "mid-life moment".