Issues related to human rights observance in Russia, the Chechnya problem, including in the context of its consideration in the European Court of Human Rights, prospects for the reform of the Council of Europe and Russia's possible contribution to the process will dominate the agenda of Mr Gil-Robles' Moscow meetings.
Moscow has noted the commissioner's unbiased position on Chechnya.
"The commissioner has taken an unbiased position on the Chechen problem from the very beginning," said a diplomat.
"Mr Gil-Robles is one of the few high-ranking European officials who has contributed to the political process in Chechnya in fact, not in word. He was one of the first officials to have backed the constitution referendum in the republic," said a Russian foreign ministry source.
Mr Gil-Robles has provided helpful recommendations to advance Russia's strategy of bringing normality to Chechnya, according to a diplomat.
Mr Gil-Robles' report will also cover Russian speakers' rights in the Baltics.
"Russian nationals' rights in the Baltic states will also be prominent at his meetings in Moscow," said the source.
This problem will be discussed in the context of the human rights reports the commissioner made after visiting the Baltic republics.
These documents address Russia's concerns on the matter. Mr Gil-Robles' reports highlight the low pace of naturalisation processes, restrictions of stateless persons' rights in Estonia, the great number of people without citizenship and the inability to pursue socio-economic and political rights by non-residents in Latvia.
Latvia has not signed the Framework Convention on the Protection of National Minorities, the fact that is also indicated in the report.
Mr Gil-Robles has raised these issues at meetings with political leaders of the countries members of the Council of Europe.
Russian speakers' rights, for example, were central on the agenda of Mr Gil-Robles' visit to Sweden on April 21-23, 2004. At a final press conference, Mr Hil Robles again highlighted serious violations in the sphere of human rights in Latvia and Estonia and asked to help these countries meet the principles stipulated in the European Convention on Human Rights and Fundamental Freedoms.