Surrey Police have confirmed that the DJ and presenter, who died last year, was interviewed under caution for alleged offences dating back to the 1970s at a children's home in Staines.
The matter was reportedly referred to the Crown Prosecution Service, Sky News reports, who advised against taking further action due to insufficient evidence.
Allegations that Savile indecently assaulted teenage girls will be made in an ITV1 documentary due to air on October 3.
Savile's nephew Roger Foster has said that his family is "disgusted and disappointed" by the claims.
"It's very, very sad you can say these things after someone's died and the law says you can't defend yourself when you're dead," he added.
It is claimed that Saville made comments in support of convicted singer Gary Glitter after his initial arrest on child pornography charges in 1997.
ITV has defended its decision to air the documentary on Savile, arguing that it is the result of an "in-depth investigation into long-standing allegations".
"The programme takes full account of the fact that Sir Jimmy is not here to defend himself against these claims," a spokesperson added.
Jimmy Savile in pictures:
Copyright: flickr/BBC Pictures