The partnership between the BBC, ITV and BT would see the development of a broadband free-to-view on-demand service via TV sets.
The BBC has split the account into two pitches. The first, which has already taken place, covers Project Canvas' identity and positioning. A result is expected shortly.
A second pitch will involve launch advertising duties for Project Canvas.
The BBC roster agencies Rainey Kelly Campbell Roalfe/Y&R and Red Bee Media and the ITV roster agency Bartle Bogle Hegarty are involved in both pitches.
Fallon, another BBC roster agency, and Abbott Mead Vickers BBDO, which handles the BT ad account, are not pitching for the accounts.
The BBC Trust launched a public consultation to assess the BBC Executive's proposals for Project Canvas late last month.
If the Trust approves Project Canvas in July, the service could be available via TV sets in early 2010.
Project: Canvas would deliver on-demand TV, such as the BBC iPlayer, and other internet content. It is understood that Project Canvas will be separate to BT Vision, BT's Freeview service.
The BBC Executive estimates that its incremental contribution to the cost of Project Canvas would amount to around £6 million over the next five years.
The proposed launch of Project Canvas follows the collapse of Project Kangaroo, a video-on-demand venture between BBC Worldwide, ITV and Channel 4.