Valieva failed a doping test at the Russian national championships in December 2021 but the result was only made known on February 8th, a day after she had helped her team win a gold medal at the Beijing Olympics.
The case, which was complicated by the fact that Valieva was 15 at the time, further damaged Russia's already tarnished record on doping prevention and shone a spotlight on the support staff of young athletes.
Six months after the test result was published, RUSADA said its probe was coming to a conclusion.
"At this stage, the investigation of this case is at its final stage. RUSADA's Investigation Department is doing a lot of work to collect information and interview the athlete's entourage," the agency said in a statement, as reported by Match TV.
"The case of a Protected Person (in this case, an Athlete who was under 16 at the time of the alleged anti-doping rule violation) requires a thorough investigation into Athlete Support Personnel.
"In the coming weeks, the results of the investigation will be submitted to the RUSADA results processing department."
Russian athletes at the Beijing Olympics were already competing without their flag and national anthem because of separate doping sanctions.
In her defence, Valieva said the positive test was the result of a mix-up with her grandfather's heart medication.
Her automatic provisional suspension was lifted by a RUSADA disciplinary committee, largely on the grounds that Valieva was under 16.
She was, therefore, able to skate in the women's single event in Beijing but, despite being the gold medal favourite, finished fourth.
The decision to allow her to compete had been upheld by the Court of Arbitration for Sport (CAS) after an appeal by the International Olympic Committee (IOC).
The World Anti-Doping Agency (WADA) later accused CAS of ignoring the world anti-doping code when it made upheld the decision and said athletes under the age of 16 should not be treated differently when it came to provisional suspensions.
As a result of Valieva's involvement, the results for the team event in Beijing remain provisional with the skaters from the second-placed United States and Japan, who finished third, still without their medals.
Canada's team finished fourth and would receive bronze medals if Russia was disqualified because of Valieva's test.
Valieva, now 16, has been active in domestic competition since the Olympics but Russian and Belarusian skaters have been banned indefinitely from international competition since the invasion of Ukraine.
In June, the International Skating Union (ISU) voted to gradually raise the minimum competition age for senior figure skating competitions from 15 to 17.
