Relations between the two countries are already warm. In an interview this week with Russia's RIA-Novosti news agency, Aliyev said ties between Moscow and Baku are at "their highest level" since the breakup of the Soviet Union 12 years ago.
But Aliyev may not base his foreign policy on Moscow relations alone. Observers say he is likely to follow in the footsteps of his father, the late Heidar Aliyev, who spent a decade in power and laid the groundwork for his son's succession last year.
The elder Aliyev was a master at using the country's vast oil reserves to carefully cultivate ties with all of the region's players -- from the United States and Russia to Turkey and Iran.
The younger Aliyev, who came to power in a controversial election last October, has pledged to pursue a similar equilibrium in his foreign policy -- one that "meets the national interests" of Azerbaijan.
Resat Rezaquliyev chairs the Eurasian Foundation for Strategic Cooperation, a Baku-based think tank. He told RFE/RL that Aliyev's Moscow visit -- which follows a recent trip to the U.S. while he was still prime minister -- does not depart from the rules set up by his father:
"The foreign policy of the former Azerbaijani president could be described as 'pluralistic.' It was a balance between the U.S. on the one hand, and Russia and Iran on the other hand. Those have been, so to speak, the two main axes of [his foreign policy.] In this regard, there is absolutely no doubt that Ilham Aliyev's visit [to Russia] comes straight from Heidar Aliyev's foreign policy," Rezaquliyev said.
Relations between Russia and Azerbaijan warmed considerably under Heidar Aliyev's rule, and Putin's rise to power gave even more impetus to bilateral ties.
The countries have resolved a long-standing dispute over the status of the Russian-manned Qabala military radar facility northwest of Baku. Azerbaijan has also gradually opened its energy market to Russian companies while discreetly taking action against Chechen separatists who had found shelter on its soil.
Baku-based independent political analyst Elhan Nuriyev tells RFE/RL he expects Aliyev's Moscow talks to boost bilateral ties even further:
"Generally speaking, I believe this visit will help bring relations between Azerbaijan and Russia to a new level. Russia is a strategic partner and an important neighbor of Azerbaijan. We are bound by commercial and economic relations and I believe the relations of friendship that exist between our two countries can only be strengthened," Nuriyev said.
There is, however, one ticklish issue that is likely to come under discussion during the Russian-Azerbaijani talks -- the possibility Washington may seek to deploy U.S. or NATO troops in Azerbaijan to guard a major oil export pipeline. That idea was raised several months ago when a high-ranking U.S. military official (General Charles Wald, the deputy chief of the U.S. European Command) said the safety of the Baku-Tbilisi-Ceyhan pipeline, which will ship Azerbaijani crude oil to Turkey via Georgia, could be entrusted to NATO.
Ahead of his visit to Moscow, Aliyev this week broke a long silence on the issue, saying such a troop deployment was "not on [Azerbaijan's foreign policy] agenda."
Russia's Interfax news agency quoted him as saying: "Azerbaijan views its own interests as a priority. When these interests coincide with those of our neighbors or great powers we cooperate; but when they do not coincide, we do not cooperate."
Rezaquliyev, however, says the question of NATO bases in Azerbaijan remains open: "Azerbaijan's [goal of integrating with] the European community and the pro-Western orientation of its foreign policy are factors that could favor the possible -- I underline, possible -- opening of NATO bases on national soil. There is no doubt about that. However, I do not believe that could take place in the near future."
Another topic Aliyev will certainly raise during the Russia talks is Azerbaijan's dispute with neighboring Armenia over the Nagorno-Karabakh enclave.
Aliyev last month blamed the Organization for Security and Cooperation in Europe, which is mediating the conflict, for failing to produce a mutually satisfactory peace plan.
His comments followed reports in the Azerbaijani media that Moscow -- which together with France and the U.S. co-chairs the OSCE's Minsk Group of nations monitoring the Karabakh peace talks -- had come out with a new plan that could help move negotiations forward.
But Rezaquliyev says the content of the Moscow plan remains a matter of widespread speculation in Baku: "The Azerbaijani press has released reports -- based, naturally, on information provided by unofficial sources -- saying that should Azerbaijan drop plans to host NATO bases on its territory, Russia would press for the return of the five [Azerbaijani] administrative districts [Armenia] has been occupying [near Nagorno-Karabakh] and the opening of transport links between Azerbaijan and Armenia. Most likely that was a test of public opinion and, as far as I am concerned, I haven't heard of anymore concrete proposals. Things remain at the level of rumors and mere scraps of information meant to feed stories to journalists."
Political analyst Nuriyev says Russia, which played a role in fueling the Armenian-Azerbaijani dispute in the late 1980s and has maintained close political and military links with Yerevan since then, has its own agenda in the South Caucasus region, which may not necessarily coincide with that of either the U.S. or Azerbaijan. He believes, however, Moscow's own security concerns could contribute to a peaceful resolution of the Karabakh dispute:
"Russia has its own vision of how the Karabakh conflict should be settled. As a major regional power in the South Caucasus, Russia knows [Karabakh] better than any one else -- I mean better than the U.S. or France. Therefore it is natural that it should want to play a leading role in the Karabakh settlement. I believe Russia can't not be interested in having the Karabakh conflict resolved, because what is at stake is its southern border. Russia has an interest in preserving stability in Azerbaijan. A stable Azerbaijan can only benefit Russia, which itself is in a state of instability -- by this I mean the situation in Chechnya and along Russia's southern border, in Daghestan and elsewhere," Nuriyev said.
As evidence that the Kremlin is keen to preserve stability in Azerbaijan, political analysts cite its expressions of support for Aliyev even before the presidential polls -- much as the U.S. stopped short of criticizing the highly controversial October elections.