The German weekly Spiegel said in its edition due out on Monday that ECB president Jean-Claude Trichet is pressing in particular for the measure to rid the central bank of the bonds it has bought under a controversial programme to provide help to eurozone banks.
It began buying sovereign bonds issued by debt-laden eurozone countries on secondary markets in the midst of the Greek debt crisis last May and has taken on a total of some 77 billion euros ($108 billion) so far.
The measure falls well outside of the central bank's core remit of maintaining price stability and stirred up a storm when outgoing German central bank chief Axel Weber issued rare public criticism of the decision.
The ECB has called repeatedly for the European Financial Stability Facility to take over the task of buying government bonds, a move that German lawmakers and economists have also expressed opposition to.
The EFSF is to be replaced by a permanent European Stability Mechanism in 2013.
According to Spiegel, the ECB request "has run into a wall in the governments of member countries."