Alexander Abramov, Evraz's chairman and founder, said in an interview with the newspaper that uniting the two businesses, with a combined market capitalisation of 12 billion pounds, would be a good idea.
I guess that this (the idea of an Evraz/Severstal combination) would have several advantages, Abramov is quoted as saying in the article.
The executive did not provide any details on how the tie-up would take place, including whether Evraz planned to launch a bid for Severstal.
Severstal said in an e-mailed statement that it does not comment on speculation.
Large-scale mergers are a rarity in the Russian steel space, where the major companies are controlled by oligarchs who created the entities in the tumultuous period following the collapse of the Soviet Union.
Severstal, Russia's second largest producer, is controlled by Alexei Mordashov, who has an $18.5 billion (11.9 billion pound) fortune according to Forbes magazine.
Evraz is controlled by several tycoons, including Roman Abramovich, who holds 35 percent, and Abramov, who owns 24 percent of the business.
Evraz's main business is in construction and railway steel, while Severstal has a stronger focus on flat steel sold to the white goods and car sectors.
(Reporting by Stephen Mangan and Alfred Kueppers; editing by Douglas Busvine)