Milosevic, suffering from a heart condition and high blood pressure, asked for a provisional release from detention in the Netherlands where he is being tried by the United Nations war crimes tribunal on genocide charges.
Mikhail Kamynin, Russian Foreign Ministry spokesman, said: "Russia has sent the necessary folder of documents to the international tribunal for the former Yugoslavia, on the basis of which the tribunal could take a decision on the temporary release of Milosevic.
"Apart from this, Milosevic himself has offered the tribunal guarantees that he will return to The Hague immediately after the completion of his treatment."
Russia and Yugoslavia were close allies in the 1990s, and Moscow opposed the Nato bombing campaign that led to Milosevic's overthrow in 2000.
Unfit to travel
However, the prosecution in Milosevic's trial, which has been going on for four years, opposes the visit and says there is no reason to believe he will return.
When asked about guaranteeing Milosevic's return, Kaymnin told the Interfax news agency: "Russia is discussing this question. All the legal aspects are being studied."
"All the legal aspects are being studied"
Russian Foreign Ministry spokesperson
The prosecution says it believes Milosevic's brother, wife and son could all be in Russia and that he could be declared unfit to travel back as soon as he arrives.
His brother Borislav, who is a former ambassador to Moscow and lives in Russia, told Ekho Moskvy radio that not admitting Milosevic to the cardiology centre would be unfair.
Borislav said: "If a man, who long ago passed 60 years of age, is not allowed to undergo treatment of any kind, then it will be a clear violation of his human rights.
"I think the tribunal has to recognise this fact and I hope it will be so."
The prosecutors have said they will oppose a release even if Russia provided guarantees to return Milosevic, saying Moscow has previously not fulfilled its promises in such cases.
Kamynin said such claims were unreasonable. "This does not reflect reality ... in this question, all conventions of international law must be examined," he said.
Milosevic, 64, is charged with genocide, crimes against humanity and war crimes in the Balkans in the 1990s.
Judges have adjourned his trial until 23 January to give Milosevic more time to rest beyond the court's three-week winter holiday.
News of Milosevic's medical appeal came amid reports that Bosnian Serb police had launched an operation in the Zepa region of eastern Bosnia, apparently on the trail of former military leader Ratko Mladic.
Mladic disappeared when Milosevic was arrested in 2001 and has been on the run since being indicted for genocide by the UN war crimes court in 1995.
However, UN prosecutor Carla Del Ponte said the former Bosnian Serb military leader was hiding in Serbia not in Bosnia.
Ratko Mladic remained in
Belgrade until 2001
Florence Hartmann, del Ponte's spokeswoman, said: "According to all our information, Mladic is in Serbia and not in Bosnia."
Del Ponte is due in Brussels on Thursday for meetings with the European Union's foreign policy chief Javier Solana, Olli Rehn, the EU enlargement commissioner, and Jaap de Hoop Scheffer, Nato's secretary-general.
She will discuss the possibilities for tracking down and arresting fugitives from the UN war crimes court.
The meetings with the EU officials are "to update the EU of the quality of the degree of cooperation provided by Serbia" with the UN court, Hartmann said.
In October, the EU opened negotiations with Serbia Montenegro about a stabilisation and association agreement, the first step to EU-membership.
Of the 161 people indicted by the International Criminal Tribunal for the Former Yugoslavia since it was created in 1993, six are still at large, all of them Serbs.