Controller Danny Cohen has stated that early plans have been made to bring Walliams to the BBC for primetime shows.
The Little Britain comedian became a Saturday night TV star earlier this year after he joined the Britain's Got Talent judging panel on ITV1.
"David is someone we're very interested in for Saturday nights," a BBC source told The Sun.
"He has the kind of warmth that will connect well with BBC One audiences. It's early days but we're hopeful of sorting something."
David Walliams recently signed up for a BBC sitcom set in an urban secondary school.
He will also narrate ITV2's upcoming Top Dog Model fronted by Stacey Solomon.