NEW YORK -- As part of its probe into the alleged Russian doping scandal, the FBI is investigating whether there is a connection to the United States, CBS News senior investigative producer Pat Milton reports.

According to a person familiar with the investigation, the FBI is investigating if there is a U.S. connection to the scandal, such as whether an American bank was used in the alleged state-sponsored doping scheme.

In addition, to determining U.S. jurisdiction or a nexus, U.S. investigators are also looking at anyone who may have benefited unfairly from the alleged scheme including athletes, coaches, anti-doping and Russian Government officials. Investigators are also looking into whether charges such as money laundering, bribery, fraud or conspiracy might have been involved, Milton reports.

The U.S. Attorney's Office for the Eastern District of New York is overseeing the inquiry into the Russian doping scandal. The prosecutors for Eastern District have also been investigating corruption within FIFA, the world soccer governing body, for the last few years.

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A former Russian anti-doping official allowed "60 Minutes" to listen to 15 hours of conversations he secretly recorded with a prominent doctor involved in the country's testing regime.

Dr. Grigory Rodchenkov shared details of a systematic cover-up in Sochi during Skype conversations with Vitaly Stepanov, a former Russian anti-doping official turned key whistleblower. The doping program reportedly involved at least 15 Russian medal winners.

"He had the ability to help to get the necessary results," Stepanov told CBS News -- referring to gold medals.

In the recordings, Rodchenkov named Russian gold medalists in three sports -- bobsled, skeleton and cross country skiing -- whose dirty drugs tests he helped cover up.

It was all part, he said, of an elaborate scheme to protect Russia's Olympic medal winners, with the help of his country's intelligence service, known as the FSB.

"FSB tried to control every single step of the anti-doping process in Sochi," Stepanov said Rodchenkov told him.

The FSB figured out a way to open bottles considered to be tamper-proof containing urine from drug-tainted athletes. Then they filled the bottles with clean urine collected from athletes before they started doping.

Rodchenkov said he then had two weeks after the Sochi games -- to make sure, in his words, people turned out to be clean before test samples were sent to the International Olympic Committee in Switzerland for storage.

CBS News also learned a recent review of blood tests in at least one Olympic event at Sochi has revealed evidence of test tampering involving Russian athletes.

The IOC issued a stern statement on Tuesday promising to step up the fight against sports doping.

The Olympics organizers said 31 athletes in six sports have tested positive in reanalysis of their doping samples from the 2008 Beijing Olympics.

The International Olympic Committee said it has opened disciplinary proceedings against the unidentified athletes from 12 countries.

Just as Russia's track and field federation was suspended by the IAAF, some of the country's winter sports bodies could be banned if allegations doping at the 2014 Sochi Olympics are proven, IOC President Thomas Bach said Wednesday.

Bach wrote in a newspaper op-ed piece that accusations that Russian officials subverted the drug-testing system at the Winter Games "represent a shocking new dimension in doping" and an "unimaginable level of criminality."

Bach said the International Olympic Committee will act with "all the appropriate measures within its powers" to deal with claims by Russia's former anti-doping director that he ran an organized doping program for Russian athletes at the Sochi Games and helped switch tainted samples for clean ones.

The IOC has asked the World Anti-Doping Agency to carry out a full-fledged investigation and plans to retest Sochi samples stored at the lab in Lausanne, Switzerland.

Bach said, if the Russian doping allegations are found to be true, the IOC would punish individual athletes and "all their entourage within its reach."

"This action could range from life-long Olympic bans for any implicated person, to tough financial sanctions, to acceptance of suspension or exclusion of entire national federations like the already existing one for the Russian Athletics Federations by the IAAF," he wrote.