According to the police source, the body of Yamadayev, who was shot on Saturday morning in Dubai, was handed over on Monday to his brother, who is in the Gulf state.
"The body of the deceased was being held in the Dubai police headquarters' morgue and was given to his brother in the evening," the police source said, dismissing newspaper reports that Yamadayev was alive and undergoing medical treatment in a Dubai hospital.
A relative told RIA Novosti on Monday that Yamadayev was alive, and the Russian Kommersant daily reported on Tuesday that his family was confident he would survive.
The daily said Yamadayev's wife had accompanied her brother-in-law Isa to a Dubai hospital on Monday evening and they confirmed to the daily that her husband was alive, but in very serious condition.
"Bullets entered his neck, shoulder and stomach, but no vital organs were touched. Sulim will live," Isa was quoted by the daily as saying.
However, a spokesman at the hospital where Yamadayev was supposedly being treated told RIA Novosti that no one under the name of Sulim Yamadayev had been registered in the hospital.
The Russian consul general in Dubai said that "no one has yet requested a death certificate under the name of Sulim Yamadayev from the consulate."
A Russian national has been arrested on suspicion of being involved in the assassination, the gulfnews.com Internet portal has reported.
Yamadayev was officially dismissed from his post as commander of the Defense Ministry's Vostok battalion last August over an alleged involvement in the 1998 abduction and murder of a Chechen businessman.
Sulim's brother Ruslan Yamadayev, a former member of the Russian parliament's lower house, was gunned down in central Moscow last September. He was a prominent opponent of Chechen President Ramzan Kadyrov, who has denied any involvement in the killing.