In a statement today, solicitors Collyer Bristow announced a request had been made for the case to be referred to the Grand Chamber.
Mosley, the former motor racing boss who was awarded damages in 2008 following publication of an article by the News of the World which he claimed breached his privacy, had made a bid to the European Court of Human Rights to make it a legal requirement for newspapers to warn subjects of articles before publication.
In a verdict published last month the Strasbourg court concluded that Article 8 of the Convention on Human Rights did not require a legally binding pre-notification requirement.
"Therefore, its absence in UK law had not breached Article 8," the court upheld unanimously.
In its judgement the court said it held the view that the concept of private life was "sufficiently well understood for newspapers and reporters to be able to identify when a publication could infringe the right to respect for private life".
Any pre-notification obligation would, it added, have to allow for an exception if public interest was at stake, the court added, and therefore a newspaper could still decide not to notify an individual if it believed that it could defend its decision.
Mosley had indicated last month his intention was to request an appeal of this decision, with an application now confirmed.
"Privacy has been the subject of considerable public and media debate in the last month and a ruling from the Grand Chamber of the Court is needed upon this important issue to close a clear gap in UK law," his laywers added in today's statement.
Free daily newsletter
If you like our news and feature articles, you can sign up to receive our free daily (Mon-Fri) email newsletter (mobile friendly).
Related articles
- Newsrewired throwback: What you learned at our previous digital journalism conference
- Three steps to protect newsrooms from press freedom attacks
- What journalists can do to prevent and fight SLAPPs
- First-party cookies: 'Get legal help to avoid fines'
- Collecting first party data: Why meaningful consent should matter to publishers