Gavin Plumb, of Harlow, Essex, denies charges relating to an alleged plot between 2 and 5 October involving the former presenter of This Morning.
Mr Plumb was not present when his application for bail was denied at Chelmsford Crown Court.
The 36-year-old was returned to custody ahead of trial in June.
He is accused of planning to assemble a "kidnap and restraint kit" and encouraging a third party to travel to the UK to carry out the alleged offences.
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A man accused of soliciting to murder and incitement to kidnap the TV presenter Holly Willoughby has been refused bail.