The Girls Aloud star sat alongside Simon Cowell, Dannii Minogue and Louis Walsh for three years on the ITV1 show. However, she stepped down in order to take up the same, ill-fated role alongside Cowell on the American version.
Despite having launched her Twitter account almost two months ago, the 27-year-old only posted her first tweet yesterday afternoon. Since then, she has used her personal feed to wish What To Expect When You're Expecting co-star Cameron Diaz a happy birthday and bemoan the lack of emoticons on the micro-blogging site.
Writing to her, the Apprentice businessman lamented her absence on the new series: "For what its worth I think Cowell shud put you back on UK X factor and bring Danni back also (sic)."
However, unsure of whether his opinions would be welcome, Sugar added: "No doubt will b told to min own biz."
The official X Factor Twitter account responded: "We love @Lord_Sugar. Man's a legend."
The X Factor continues on Saturday at 8pm on ITV1.
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