The celebrity couple using an injunction to prevent press revelations about their private life are also seeking to remove internet links from search engine Google, the Daily Mail reports.
It says that a firm specialising in online privacy has asked the web giant to remove 150 search links which mention the married man allegedly involved in a threesome with another couple.
The story has been reported by newspapers in the UK and Scotland, and by a London-based political blog.
But publishers, and individuals, in England and Wales risk a fine and imprisonment if they breach the interim order preventing publication of details about those involved in the alleged menage a trois.
Complaints have reportedly been lodged by the company Web Sheriff.
The Sun is set to go to court on Friday in a fresh bid to get the interim injunction removed.
It is likely to argue that the knowledge of those involved in the case is now so widespread that the information can no longer be said to be private.
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