The body of Miss Yeates was found on Christmas Day after an eight-day hunt The Sun and Daily Mirror are facing contempt of court proceedings over the way they reported the hunt for the killer of Jo Yeates last December.
The case is being brought by Attorney General Dominic Grieve.
It concerns stories about the arrest of the Bristol landscape architect’s landlord, Chris Jefferies, who was later released without charge.
Another man has admitted the manslaughter of Miss Yeates but denies murder and is awaiting trial.
Miss Yeates vanished after returning to her basement flat in Bristol’s Clifton area on 17 December. Her body was found on a grass verge about three miles away in Failand on Christmas Day.
BBC legal correspondent Clive Coleman said it was extremely rare for contempt of court proceedings to be brought against newspapers.
It only happens when the reporting is thought to have created a “substantial risk” of seriously prejudicing a fair trial.
In this particular case it is especially unusual as the attorney general is acting in respect of someone who was not charged, our correspondent added.
The first hearing in the case is taking place at the High Court later and the tabloids could be fined or individuals at the papers imprisoned if the case is proved.
It comes after lawyers for Mr Jefferies launched separate libel and privacy claims against the Sun, Daily Mirror, Daily Mail, Daily Express and Daily Star.
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