Russian athletes Tatyana Lebedeva (gold), Irina Simagina (silver) and Tatyana Kotova (bronze) won the medals but have since failed drugs tests in other competitions held after the Athens Games.
Thirteen years after the Athens Games, Anju, who had finished fifth with an effort of 6.83m, will launch her bid to claim an Olympic medal together with Australia's Bronwyn Thompson and Britain's Jade Johnson who had finished fourth and sixth respectively.
"I suspect all the three Russians did not win their medals through clean means. They failed dope tests later on and there is this widespread doping scandal in Russia. These are strong enough indications that all the three were not clean during Athens Olympics," Anju told PTI from Bangalore.
"I feel I could have been India's first Olympic medallist in athletics (by winning a medal in Athens). I have been robbed of that glory and the moment of winning an Olympic medal for the country by them (the Russians). The country has been robbed of an Olympic medal," she added.
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"I have made contacts with Thompson and Johnson and we will take up the matter and represent our case together. I have been told that the Australian athletics body will have a meeting on March 31 to take up the issue and I will be meeting AFI and Sports Ministry officials this weekend in this regard," she said.
However, samples of the three Russians from the 2004 Athens Games might have since been destroyed since the 10-year statute of limitations has passed, but Anju said she will ask for investigations based on available evidence.
"When some of the old samples of 2004 Athens Games were re-tested in 2012, the samples of these three Russians were not tested. So, you cannot say that they were clean during the Athens long jump event.
Earlier, the IOC kept all the dope samples in their laboratory at Lausanne for eight years to be re-tested again and later on the limitation period was extended to 10 years.
So, it is practically impossible to find the 2004 Athens Games dope samples for re-resting.