The as-yet unpublished assessment from the Bundesverfassungsschutz, the domestic intelligence agency, dedicates six pages to "openly extremist structures" in The Left, or Die Linke in German, according to the Wednesday edition of Bild.
Interior Minister Wolfgang Schäuble will officially present the report on Thursday in Berlin.
Schäuble, a member of the conservative Christian Democrat party, has described parts of The Left party as "a clear extremist threat." Germany's domestic intelligence services have been monitoring individual members since parts of the political party was formed from the ashes of the East German communist party.
Bild reported that the largest subgroup within The Left mentioned in the intelligence report, the so-called Communist Platform (KPF) is described as openly fighting for the overthrow of capitalism. KPF has 840 members in The Left, according to the report.
About 60 people reportedly belong to the Marxist Forum, described as a collective of orthodox Communist sympathizers that includes members of the former Communist party from East Germany.
A third group, the 120-member Geraer Dialogue/Socialist Dialogue (GD/SD), seeks to "fight outside of the parliament for social changes," according to the newspaper's report. The report also names the 550-member Socialist Leftists and the 420-member Workers' Alliance Cuba Si.
The Left party was formed last year out of a merger between the Party of Democratic Socialism (PDS), the reformed communist party from East Germany, and a small left-wing party in western Germany made up of discontented former members of the centre-left Social Democratic Party (SPD).
About 10,000 people have joined since the party's founding - even as Germany's established political parties lose members.