The natural family of Billie-Jo Jenkins wants the law changed so it can bring a civil action against her foster father Sion Jenkins, it has told the BBC.
Billie-Jo Jenkins was killed in February 1997
Mr Jenkins was cleared at a second retrial in February of killing the 13-year-old in East Sussex in 1997.
The teenager's relatives want a civil case to establish liability, but a six-year limit on bringing proceedings is preventing that.
Mr Jenkins was "appalled" at the move, his friend Bob Woffinden said.
Billie-Jo's natural family, from east London, said it was consulting lawyers about its options.
The schoolgirl was beaten to death at her foster parents' home in Hastings in February 1997.
Mr Jenkins, now living in Hampshire, served six years for her murder before being freed on appeal.
He was then formally acquitted after juries in two re-trials failed to reach a verdict.
Billie-Jo's natural father Bill died of cancer in the summer.
Other relatives say he wanted to bring a civil action, but they only considered the move after criminal proceedings concluded in February, nine years after her murder.
Billie-Jo's aunt, Maggie Coster, told the BBC: "All we're interested in is getting some sort of justice.
"She was a 13-year-old child brutally murdered - battered - and there's nobody to answer for it."
Mr Woffinden, a journalist who befriended Mr Jenkins during the court cases and became his media adviser and campaigner, said in response: "If anything were to happen it would obviously be very vigorously contested.
"There's no point in going down the same blind alley again."
Mr Woffinden said Mr Jenkins' concern was that the murder should be fully re-investigated by the police.
The government has said it will consult on plans to change the limitation period in civil cases, but it is not clear how far the reforms will go and whether the new rules will apply retrospectively.
Next year the Law Lords will rule on the case of serial rapist Iorworth Hoare, who won £7 million on the lottery.
One of his victims was prevented from suing him because the attack happened 18 years ago.