Local business daily Vedomosti cited an unamed source saying that the shares would be floated in Moscow or London, and the listing was expected to raise about $250 million. NCSP officials have declined to comment on the possible public offering.
Novorossiysk, on Russia's Black Sea coast, specializes in crude oil, refined products, chemicals, grains and containers.
NCSP is largely owned by a group of Russian businessmen while the state of Novorossiysk controls a minority 20% stake.
NCSP has reportedly informed authorities that shareholders will hold an extraordinary meeting next month to decide whether to proceed with an IPO.
Russia's First Deputy Prime Minister Sergei Ivanov and Transport Minister Igor Levitin had recently announced a modernization program for Russia's Black Sea ports.
Reports said that the plans are similar to the programme for the accelerated expansion of Russia's Baltic ports.
Russian Black Sea ports currently handle more than a third of Russia's maritime exports in terms of cargo tonnage.
Total export cargo volumes were 160 million metric metric tonnes (mt) in 2006. They are projected to rise to more than 250 million mt a year by 2010.
The port modernization program is scheduled to double existing export handling capacities.
More than half the export volumes are currently being handled by Novorossiysk, which has seen serious congestion.
The development program for the Russian Black Sea region calls for the transfer of some shipping to other ports, leaving Novorossiysk to concentrate on oil, grain and container cargoes.
Both the Deputy Prime Minister and Transport Minister have called for Novorossiysk to compete with Romania's port of Constanta for container traffic.