During his two-day unofficial visit, Nikolic will discuss the situation surrounding the Serbian province of Kosovo, whose future independence is opposed by Belgrade.
Nikolic is an ardent supporter of closer ties with Russia, including in the military sphere, and has expressed his appreciation for Moscow's consistent backing of Belgrade over the Kosovo issue.
As a presidential contender, Nikolic's main rival is Serbian President Boris Tadic. Both politicians currently enjoy equal voter support in the run up to the February 3 elections.
"The Kosovo problem could well push the Serbian electorate toward the radicals," said Konstantin Zatulin, director of the Institute for CIS Studies, adding that Russia was currently enjoying tremendous popularity among Serbians.
Tadic held talks with Russia's leadership in Moscow last week. Russia's Gazprom Neft signed a deal on the purchase of a 51% stake in the Serbia state-owned oil monopoly Naftna Industrija Srbije (NIS) during talks between the two countries' leaders on Friday.
Russia and Serbia also signed an oil and natural gas cooperation agreement on the construction of the Serbian section of the South Stream gas pipeline system.
Nikolic, seen as an anti-Western far-right figure, gained a five-point advantage in Sunday's first voting round, sparking concerns in the EU. Although the president's powers are limited in Serbia, the office has important symbolic significance.