Minogue was in negotiations to reprise her role on the show after last year's panellist Kelly Rowland ruled herself out.
The Australian entertained the idea of a return despite disclosures that she and show boss Simon Cowell had an affair. But discussions have now foundered.
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Tuesday night's weather for the west of the region
Tuesday night's weather for the east of the region
An elderly woman sold her bungalow to move into sheltered housing in Kent, only to be told 5 months later that support may be taken away