This comes after the International Olympic Committee (IOC) revealed last week that retests of 454 samples using new technology had been completed in conjunction with the World Anti-Doping Agency (WADA), focusing on those who are likely to compete at Rio 2016.
A total of 31 athletes spanning 12 National Olympic Committees (NOCs) and six sports were implicated, the IOC said.
All those NOCs are currently being notified - with retesting of B-samples expected later this month and the names set to be formally confirmed soon after.
But Russian state television and the TASS news agency have now published a list of athletes they say have been notified of failures, citing an unnamed source in the Russian Olympic Committee (ROC).
These include Yuliya Chermoshanskaya, a member of the gold medal winning 4x100 metres relay quartet, and Anastasia Kapachinskaya and Tatiana Firova, who both won silver as part of the 4x400m relay team.
Others include bronze medal winning high jumper Anna Chicherova, who has since won gold at the London 2012 Olympic Games, javelin silver medallist and 2011 world champion Maria Abakumova and bronze medal winning 50km racewalker Denis Nizhegorodov.
Yekaterina Volkova, the 2007 world champion who won bronze in the 3000m steeplechase behind world record breaking team-mate Gulnara Galkina-Samitova, is also named, as is Denis Alexeev, a member of the bronze medal winning 4x400m quartet.
The list is completed by two weightlifters in under 58 kilogram silver medallist Marina Shainova and under 75kg third placed finisher Nadezhda Evstyukhina.
Belgium stand poised to claim 4x100m relay gold if Russia's women are disqualified.
Names of six non-medal winners have also been published, including three more athletes in 2009 world bronze medal winning decathlete Alexander Pogorelov, 2006 European 10,000m champion Inga Abitova and shot putter Ivan Yushkov.
Rower Alexander Kornilov, a member of the Russian eight which won a silver medal at last week's European Championships, is also implicated.
"The ROC has received the respective documents," a member of the National Olympic Committee told TASS.
Russian high jump coach Yevgeniy Zagorulko has already revealed how Chicherova has been notified.
"Three days ago, Anna received a notice that her doping sample from the Beijing Olympics tested positive after a re-check and she called me," the coach told TASS.
"So far, this is at the development stage and this has not yet been finally confirmed - but we all are aware of this and are dealing with the issue."
International Association of Athletics Federations (IAAF) anti-doping rules appear to suggest that any athlete retrospectively caught doping will be stripped of all subsequent results, meaning that, if her positive sample is confirmed, Chicherova would forfeit her London 2012 title.
The IOC have also said how any athlete implicated in the Beijing 2008 retests will also have their London 2012 results immediately re-analysed, so Chicherova's gold medal winning London 2012 performance will come under scrutiny anyway.
insidethegames has been told by the IAAF that the IOC were acting on athlete-specific intelligence provided to them by the world governing body.
Chicherova's training group under Zegorulko - based in 2014 Winter Olympic host city Sochi - also included Athens 2004 high jump champion Yelena Slesarenko, who came fourth behind Chicherova four years later so could be promoted to bronze.
If today's reports are confirmed, it would be a further blow to the world's largest nation as the All-Russia Athletic Federation seek to have its suspension lifted by the IAAF in time for athletes to compete at Rio 2016.
This followed last year's allegations of systemic and state-sponsored doping across Russian athletics published by the WADA Independent Commission.
“The Ministry of Sport is extremely disappointed that Russian athletes are among those found to have violated anti-doping rules at the 2008 Beijing Olympics after re-testing their samples," the body said in a statement sent toinsidethegames today.
"All the athletes found cheating should face corresponding sanctions.
"We have taken numerous steps to eradicate the issue of doping, and understand that the roots of the problem, particularly in athletics, go back to the past.
"Since 2008, when the Ministry of Sport was formed, the Russian anti-doping system has been overhauled: a national anti-doping agency has been created; legislation against doping has been tightened; and considerable work has been taken to change public opinion and develop a zero-tolerance stance on doping.
"However, this is an ongoing issue that we are committed to tackling - we are continuing to improve the work of Russian anti-doping services, ensuring they are effective, transparent and independent.”
ARAF has said this evening that no athlete implicated in a past doping scandal will be able to compete in Rio.
Russia finished second on the athletics medals table at Beijing 2008 with six gold, five silver and seven bronzes.
Of the six gold medals won by the country in athletics, race-walkers Valeriy Borchin and Olga Kaniskina have since been implicated in doping scandals and have served bans - although their failures each came later so they are not currently expected to be stripped of Beijing 2008 gold.
Russia finished third in the overall Beijing medals table with 23 gold, 21 silver and 29 bronze.
They won medals in a total of 16 sports: aquatics, archery, athletics, basketball, boxing, canoeing, cycling, fencing, gymnastics, handball, modern pentathlon, shooting, tennis, volleyball, weightlifting and wrestling.
It is not yet clear which other countries are implicated in the Beijing failures.
Several NOCs, including Britain, Australia, France and South Africa, have already said publicly how they have not been contacted by the IOC.