The woman reported allegations on Monday that Myra Hindley and Ian Brady and a third person tried to snatch her in 1964.
It is understood the unnamed third person is still alive.
Detectives are taking the woman's claims seriously. The woman, now 51, told them the attempt was made in Denton, Greater Manchester.
Five killings
Police said they had not yet taken a formal statement from the woman, but they are "actively investigating" the claim.
Hindley and Brady were jailed for life after torturing and killing five children during the 1960s.
They buried the bodies on Saddleworth Moor, in Greater Manchester.
Hindley died in hospital last month at the age of 60. Brady is still serving life in Ashworth High Security Hospital on Merseyside.
Murder witnessed
The couple were caught after they killed Edward Evans, a 17-year-old they met in Manchester and lured back to their council home in Hattersley, near Hyde.
Brady murdered the teenager with an axe in the front room of the house while David Smith, Myra's brother-in-law, was there.
Mr Smith returned home and contacted the police.
He also told officers that Brady had talked of other murders and of burying bodies on Saddleworth Moor, which he had earlier dismissed as fantasies.
Brady was also convicted at the trial of killing 12-year-old John Kilbride.
In 1987 Brady confessed to the murders of Pauline Reade, 16, and Keith Bennett, 12.