According to the News Of The World the singer, who joined the Strictly judges in 2009 after winning the series two years earlier, has been in talks with ITV bosses about being a part of the show.
The paper reports that show bosses are battling to find somebody who has the star power of Cheryl Cole, following reports that she is quitting the UK show to be a judge on the US version.
Alesha is one of several female singers who have been linked with the show in recent weeks, including Lily Allen, Saturdays singer Frankie Sandford and N-Dubz star Tulisa.
“Cheryl leaves a massive void on the panel and there’s a serious hunt going on right now,” a source said.
“The obvious advantage of Alesha is that she’s young, sexy and confident and already has experience on a judging panel.
“But that’s also a downside because they like the idea of finding someone fresh. Nothing has been decided yet but it’s close to panic stations because auditions are starting soon.”
Take That frontman Gary Barlow has also been rumoured to be joining the panel as a replacement for Simon Cowell, who is also judging the US version of the show. He is expected to return to the UK series at the live finals stage.