Fiona Bruce is in discussions about taking over as presenter of the discussion programme Question Time, BBC News understands.
BBC media editor Amol Rajan said negotiations with Bruce, who presents the News at Six and Ten as well as the Antiques Roadshow, were continuing.
Current host David Dimbleby will leave the show in December after 24 years.
If Bruce succeeds Dimbleby, she will become the first female host in the show’s 40-year history.
The BBC’s media editor said Bruce auditioned alongside several other leading broadcasters at the corporation for the job.
Senior figures at the BBC were known to want an established figure who had experience on BBC One, our correspondent added.
Bruce has worked at the BBC since 1990, when she began her career as a researcher on Panorama.
The 54-year-old went on to become a reporter on the programme and also on Newsnight.
Bruce also co-hosted Crimewatch on BBC One for eight years.
In 2001, she became the first female presenter to be part of the BBC’s general election studio team.