The company is believed to be talking to restructuring firms, one of which is thought to include a Company Voluntary Arrangement (CVA), a controversial insolvency procedure used to shed under-performing sites, the Press Association reports.
Claire's has more than 350 stores in the UK and dozens of concessions, according to its most recent accounts.
Hundreds of jobs could be at risk if the chain presses ahead with a CVA.
The news comes just days after the chain's US parent company announced that it had emerged from Chapter 11 protection after filing for bankruptcy earlier this year.
Investment funds Elliott Management and Monarch have seized control of the US arm through a painful restructuring.
Claire's could join a growing number of recognisable high street names to scale back its store estate, as consumers increasingly shop online.
CVAs have hit the headlines this year after the procedure was used by the likes of New Look, Jamie's Italian and Mothercare to shed sites and gain rent reductions.
It is understood that the talks are at a preliminary stage.
Fears that the UK fashion accessories chain could disappear from the high streets grew earlier this year after its US parent, Claire's Stores Inc, filed for bankruptcy.
The US company announced last week that it has now emerged from Chapter 11 protection, having restructured almost $2 billion (£1.5 billion) of debt.
Chief executive Ron Marshall said Claire's had emerged as a "healthier, more profitable company" after eliminating debt and gaining access to 575 million US dollars in new capital.
However, Claire's has previously stressed that its European operations would not be affected by the American business.
Additional reporting by Press Association.
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