Medvedev and Cuban President Raul Castro are expected to sign trade deals on nickel mining and oil exploration, the BBC reported Thursday.
Russia companies reportedly are interested in drilling for oil in Cuban waters and investing in a nickel processing plant.
Before arriving in Havana, the Russian leader was in Venezuela, where he and President Hugo Chavez signed a deal on promoting nuclear energy, the British network reported.
Boosting trade between Russia and Latin America, which could reach $15 billion this year, is a focus of the Russian trip.
Before visiting Venezuela, the Russian president was in Brazil, where he and President Luiz Inacio Lula da Silva held trade talks.