Egon Zehnder, the headhunter firm which recently contributed to the hunt for the new BBC director general, is reportedly now coordinating the search for the new person to lead All3Media.
According to The Guardian, Davie was shortlisted by Egon Zehnder for the BBC director general role, but did not make it through to the final round of interviews.
The role eventually went to George Entwistle, the director of BBC Vision.
Sources told the paper that Egon Zehnder has retained Davie on its radar and put him forward for the All3Media chief executive search.
But Davie is also thought to be in the running to lead a revamped BBC Worldwide, under plans being considered by Entwistle to bring the BBC's commercial arm closer to the main BBC operation.
Entwistle is understood to have already put the Worldwide plans forward to the BBC Trust for approval, but he cannot take any action until he officially takes over from current BBC director general Mark Thompson in September.
That could be enough time for All3Media to turn Davie's head and encourage him to jump ship to the commercial sector.
Private equity house Permira, which is the majority owner of All3Media, is looking to find the right candidate to succeed chief executive Steve Morrison.
Morrison helped found the company in 2003 and still has a minority shareholding. He will remain with the company as chairman.
Neither All3Media or Davie have commented on the report.
> All3Media international head to join Sony as chief creative officer
> The Only Way Is Essex maker All3Media to launch TV on-demand service
> Midsomer Murders maker calls off sale plans