Rotherham Council has asked a High Court judge to intervene the protect the girl.
Mr Justice Keehan has analysed preliminary issues at hearings in the Family Division of the High Court in London on Thursday.
Decisions are expected to be made in the near future following a final hearing.
In late 2014, Mr Justice Keehan made civil court orders against 10 men from the Birmingham area, who had sexually exploited a teenage girl who was in the care of the local authority, following ‘bold and novel’ legal moves made by council bosses.
Police said there was insufficient evidence to secure criminal convictions against the men.
But Mr Justice Keehan imposed injunctions barring the men from contacting the teenager, and from approaching girls they did not know, following applications by Birmingham City Council.
He also ruled that the 10 men, who could be jailed for being in contempt of court if they are found to have breached the orders, could be identified in media reports.
Lawyers representing Rotherham Council now want a judge to take similar steps.
Mr Justice Keehan has ruled that neither the teenager nor the men – in the Rotherham case – can be identified at this stage.
Barrister Rebecca Foulkes, who is leading Rotherham Council’s legal team, said council bosses wanted a judge to make ‘injunctive orders’ against the four men, with the application backed by the girl’s parents.
The application comes in the wake of the Rotherham child abuse scandal.