The Times said "a person with direct knowledge of the matter" told of the swap.
It would be carried out over the objections of Deutsche Bundesbank, Germany's central bank, which fears the move will discourage investors from purchasing debt from other struggling European countries.
The Times said its source had informed the Frankfurter Allgemeine newspaper of the development.
If the ECB avoids a loss, the reasoning goes, then private investors will have to accept a larger share of the devaluation of debt, should that occur.
Greece is negotiating with private bondholders to have them accept a voluntary devaluation of 70 percent on their holdings.
That deal would reduce Greece's debt obligations by about $130 billion.
Greece is working through deals to put its finances in order to qualify for a $170 billion international loan. Without the loan, officials say, Greece will default on its debts March 20.
The ECB, which could make the swap as early as Monday, holds about $66 billion in Greek bonds.