Savile volunteered at the Leeds General Infirmary during the 1960s and 70s and undertook charity work until his death in October 2011.
A spokesman for Leeds Teaching Hospitals NHS Trust said:
We are shocked at the nature and extent of the very serious allegations made against Jimmy Savile which were revealed by the Metropolitan Police on Wednesday. We have made contact with the police and they will be meeting with us to discuss their investigation.
The Trust does not have any record of complaints about Jimmy Savile’s behaviour made during the time he was a volunteer and charity supporter at Leeds General Infirmary or at any of our other hospitals.
As a result of the TV documentary and subsequent media publicity we have, however, been contacted by two individuals, one of whom wishes to remain anonymous, about incidents said to have occurred in the 1970s.
Clearly this whole matter needs to be looked into fully and we will give every co-operation to the police, who are best placed to do so.
We would urge anyone with specific concerns about Jimmy Savile’s behaviour to contact the police via the NSPCC helpline, 0808 800 5000.
North Yorkshire Police have also confirmed that they have received a report of a historic sexual offence linked to the Jimmy Savile enquiry. The offence involving a young girl is alleged to have taken place in Scarborough in the late-1980s
This further allegation is now being investigated by the MET Police.