The office's president Andreas Mundt said on Monday that a linkage between the two would have to be looked at “very carefully” and could have implications for competition.
He emphasized that his agency is not yet looking into the situation since nothing has been officially announced.
“So far, we only know speculation from the press,” Mundt said.
Mundt's comments come as reports increase that the two companies want to create a close partnership that could include an exchange of ownership stakes.
Der Spiegel magazine has reported that RWE head Jürge Großmann met Alexey Miller, the head of Gazprom, in Paris on Friday to discuss potential investment opportunities that could see the Russian gas producer take a stake in RWE, Germany's second-largest power supplier.
Gazprom has been expressing its interest in the German energy market for several months, especially as Germany announced its pullout from nuclear energy.
But Germany is not the only target country for Miller and his company. In recent days, company officials have met with the French energy company GDF Suez and the Düsseldorf-based E.ON energy concern.
The Federal Ministry of Economics and Technology said it was exploring whether cooperation between the two companies could violate foreign trade laws – although in principle, Germany is open to foreign investors.