The singer, who currently stars on rival show Strictly Come Dancing, has allegedly met with ITV bosses to discuss joining the judging panel.
It is thought that Dixon would replace Cheryl Cole, who is widely expected to be a judge on the US version when it launches this autumn. Producers have apparently struggled to find someone to match Cole's star quality.
"Cheryl leaves a massive void on the panel and there's a serious hunt going on right now," a source told the News of the World.
"They're worried that without Simon on the panel either they need to find someone with a strong voice and personality who can blossom into a star. 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."
Meanwhile, Gary Barlow is said to be in "advanced talks" to replace Simon Cowell, who will no longer appear as a weekly judge as he concentrates on the show's US launch.
"Gary and Alesha get on brilliantly and they could really be a winning combo," the source added.
Lily Allen and The Saturdays star Frankie Sandford have also been linked to the role.