The officer, who was from West Yorkshire Police, was accused of contacting Surrey Police before they questioned Savile over alleged sexual offences in 2009.
But the Independent Police Complaints Commission (IPCC) found that if the officer was still working, he would have “no case to answer”.
The IPCC interviewed him under caution and spoke to various witnesses, including a number of regular attendees of the so-called Friday Morning Club held at Savile’s flat in Leeds.
While the inspector accepted he made a phone call in June 2009 to Surrey Police, he did so solely to pass on Savile’s contact details.
It was found that he made no direct enquiries into the reasons why the force sought to contact Savile, and was unaware of their criminal investigation at the time.
A statement from the IPCC said: “The IPCC investigator considered it ill-judged of the former inspector in telling his counterpart at Surrey Police of his friendship with Savile, as it served to make the Surrey officer suspicious of his motives and to rightly report the conversation.
“However, there was no evidence that the inspector had tried to influence the police.”
The release of the investigation report comes after the IPCC confirmed last month the inspector had been cleared of misconduct.
Another claim it looked at was whether he had any letters accusing Savile of offences.
Such letters were said to have been referred to at the Friday Morning Club, a gathering which the inspector had attended.
But the investigation found “no evidence” of these having been shared with the inspector either at the club, or privately.
West Yorkshire Police was ordered by the IPCC in 2013 to refer the conduct of the officer.
In 2013, the force also conducted its own review into its contacts with Savile, which concluded there was no evidence the TV star was protected from arrest or prosecution as a result of his relationship with West Yorkshire Police or officers.
The West Yorkshire review looked at a range of allegations about the force’s contact with Savile, including claims made to Operation Yewtree investigators and others mentioned in a report on Savile’s offending by Her Majesty’s Inspectorate of Constabulary.
These ranged from officers attending Savile’s Friday Morning Club to claims he had been interviewed by officers from the Yorkshire Ripper inquiry.
Police officers were among guests at the Friday Morning Club meetings, which were held at Savile’s luxury penthouse, and are believed to have taken place for around 20 years.
But the report found no evidence to conclude any misconduct in relation to the meetings and said there was no evidence of any allegation being made to the force at all before he died.