The woman was 8 at the time, possibly making her Savile's youngest alleged victim, the Daily Mirror reported Monday.
Numerous reports of sexual assaults allegedly committed by Savile have surfaced since his death at the age of 84 in October 2011.
Scotland Yard is investigating complaints against Savile that span a half-century, officials said.
Authorities have said hundreds of cases of alleged abuse were involved.
Liz Dux, an attorney representing the woman, said her client was hospitalized at Stoke Mandeville Hospital when she was molested by Savile, a popular media figure.
Dux's law firm is representing 36 people who say they were Savile abuse victims.
Savile's oceanfront apartment in North Yorkshire, where he entertained police friends, has reportedly not been searched even though it is being sold, raising fears that some evidence could be lost, the report said.
Yorkshire Member of Parliament Robert Goodwill said the flat should be checked 'before any evidence can be compromised."
A spokesman for the metropolitan police said, "We are not saying where we are searching."