The Yorkshire Post said a well-placed source told the newspaper police officers investigated both men but claims no action was ever taken after it was referred up the chain in South Yorkshire Police.
South Yorkshire Police said it carried out extensive checks and has no record of any investigation.
An IPCC spokesman said: “The IPCC received a letter from John Mann MP containing allegations that Sir Norman Bettison had been involved in a theft in 1987 while he was a serving officer with South Yorkshire Police.
“The IPCC instructed South Yorkshire Police to make a referral of the allegation in order for an assessment to be conducted to determine whether this was a matter which should be independently investigated by the IPCC.
“After careful consideration the IPCC has concluded that this is a matter which can be referred back to the police service.
“It relates to allegations of a minor criminal offence 25 years ago and is not connected to other matters in relation to Sir Norman and Hillsborough, where it is clearly in the public interest for the IPCC to independently investigate matters which took place a long time ago.”
Mr Bettison resigned as chief constable of West Yorkshire Police in October after pressure over his alleged role in the cover-up of the Hillsborough disaster.
He is currently under investigation by the IPCC for his role in the aftermath of the disaster and for allegations he tried to interfere with West Yorkshire Police referring him to the IPCC.
Mr Bettison, Merseyside chief constable between 1998 and 2005, denies any wrongdoing.