Mrs McConville was abducted from her home in west Belfast by the IRA in 1972 before being shot and secretly buried.
Sinn Féin president Gerry Adams was arrested last year over her murder.
But the Public Prosecution Service (PPS) has said he will not be charged.
Mr Adams said Tuesday's announcement by the PPS was "long overdue".
Mrs McConville was one of the Disappeared. Nobody has ever been charged with her murder.
Helen McKendry, one of her daughters, said in 2010 that she planned a civil action against Mr Adams in relation to the killing.
She has now instructed McCue & Partners to look into the possibility of taking a civil action.
The London firm represented 12 families of the victims of the 1998 Omagh bomb in a civil prosecution in which they were awarded £1.6m damages.
A representative of the firm said it had been asked "to determine the possibility of bringing a civil action against those allegedly responsible" for Mrs McConville's kidnapping, disappearance and murder.
"The family have waited patiently for the [PPS] decision," the representative added.
"They now wish to determine whether other judicial avenues are open to them to secure justice and accountability for Jean's murder."
Mrs McKendry said she had wanted to work with McCue & Partners because of its work for the Omagh bomb victims' families.
She said she "can't blame" the PPS or the police for deciding not to charge Mr Adams and six others.
"If there are witnesses out there who won't come forward to give statements, what can the police do?" she told BBC Radio Ulster's Talkback programme.
"I believe the only thing I can do now is take civil action, this is the only way I can go forward.
"It's been a long road - 43 years - and all I want is the truth about my mother, not just for my sake but for my children and my grandchildren."
Mrs McKendry's husband Seamus said: "Helen has waited a lifetime - she just wants justice.
"We do not believe in kangaroo justice. We believe in due process, and had that been administered to her mother she would probably still be alive."
A law firm that represented families of victims of the Omagh bombing is exploring the possibility of legal action against people allegedly responsible for the murder of Jean McConville.