Recent reports have named the popstar as a possible replacement for Cheryl Cole on ITV's The X Factor. In a magazine interview, Dixon also praised Simon Cowell's show for allowing the judges to be "more creative" with their mentoring roles.
"She is not the most important part of the Strictly judging lineup and the show's success does not depend on her," an insider told The Sun. "It is not on for Alesha to woo The X Factor.
"She is a judge on the biggest entertainment show on the BBC and should be proud of that - not making public pronouncements about its biggest rival."
The source went on to claim that bosses had demanded a meeting with Dixon's agent to discuss the situation.
"If she hadn't committed to the show immediately they were prepared to show her the door - even if she didn't get a job offer from The X Factor," they continued. "What was most galling about it was that the BBC supported Alesha over the past few years when she got a lot of flack about joining Strictly."
The 32-year-old's manager Malcolm Blair added: "Contrary to recent speculation, Alesha is committed to Strictly and looks forward to taking her place on the judges' panel when the show returns."
Simon Cowell has confirmed that Gary Barlow will join The X Factor panel, while an official announcement is expected "soon" ahead of the first auditions in Manchester on May 18.
> Take a look at our complete coverage of The X Factor