It's been variously reported that X Factor boss Simon Cowell has been keen to get Rita on the X Factor, describing her as "fair game" after being impressed with the singer's debut on The Voice this year.
But while Simon's been after Rita, ITV are said to be against the idea.
A source said recently: "ITV see X Factor as vastly superior to The Voice. They don’t want a judge who they see as a cast-off."
However Rita's fellow - at least as of now - Voice UK coach Will.i.am has reportedly backed Rita to switch shows.
“If it’s the best thing for her career, then she should go," he was quoted as saying.
But it may be that Rita ends up saying no to BOTH The X Factor and ITV in order to focus on her music.
An insider told the Daily Star newspaper last weekend: “Rita’s second album has already been pushed back almost a year and she wants to concentrate on promoting her record, especially in the US where she is still trying to crack the market.
“She knows a permanent role on the X Factor will be too big a commitment back home and stop her international music ambitions.”
In our polls over the past few weeks, an overwhelming 80% wanted Rita to stick around with 57% saying she should stay on The Voice UK rather than switch to The X Factor.
Which show would you prefer to see Rita on? Vote in our poll if you've not done so already here...
The judges for both The Voice UK and X Factor will be confirmed in due course.