The announcement from the firm came as tension skyrockets between Russia and the West over Ukraine and as western energy dependence on Russia comes under scrutiny.
Mr Schroeder and other candidates on the list of names released in a company statement must still be confirmed at the next general meeting of shareholders in June.
Despite worsening relations between Germany and Russia, Mr Schroeder is chairman of the board of directors of Russian oil company Rosneft.
He is also on the shareholders committee of Nord Stream 2, a Russian-German gas pipeline also built by Gazprom.
The former chancellor's pro-Kremlin stance has often angered Berlin, a sentiment which has grown amid fears of a Russian invasion on Ukraine.
Mr Schroeder recently defended Moscow's decision to mass tens of thousands of Russian soldiers on Ukraine's border.
Germany's current chancellor, Olaf Scholz, had to publicly assure Germans that he will not be influenced by his predecessor on the current crisis.
“I did not ask him for advice, he did not give me any either,” Mr Scholz said.
He is due to visit Kiev and Moscow this month to discuss the crisis on the Russia-Ukraine border.
Liberal FDP member of Parliament Marie-Agnes Strack Zimmermann called for Mr Schroeder's privileges as former chancellor to be questioned after Gazprom's announcement on Friday.
She accused him on Twitter of “harming” the country.
Germany closely co-operates with Moscow in energy, importing 55 per cent of its gas from Russia.
But Berlin now wants to develop the construction of liquefied gas terminals to reduce its energy dependency on Russia.
Mr Schroeder was chancellor from 1998 to 2005 and chairman of the Social Democratic Party from 1999 to 2004.