Simon Cowell has previously shown interest in buying the Top of the Pops franchise, while Channel 5 owner Richard Desmond revealed that he wanted to revive the show last year.
Wadsworth told Music Week: "We are not saying 'bring back TOTP' but there is a gap, and the BBC is missing a trick by not having a show."
BBC 6 Music presenter Lauren Laverne agreed, but said that the format would need to change in order to attract new viewers.
"I think now more than ever we need Top of the Pops back. I don't know whether you'd want to do it in a chart-based way or more of some kind of social media you could base it on."
However, the BBC cooled any rumours of a return for the show, with a spokesperson saying: "We are constantly in discussion with the music industry, but there are currently no plans to bring back Top of the Pops."
The final official Top of the Pops episode aired on July 30, 2006, though the traditional special editions continue to be aired at Christmas.
Watch a clip of Duran Duran on a 1982 edition Top of the Pops below: