An announcement of the debate is expected this week, according to the Sunday Times.
The paper says Labour sources claim that the Tory leadership has resisted signing up to a series of TV debates between cabinet ministers and their counterparts in opposing parties.
This comes as the Tories confirmed they would only make limited spending cuts this summer and only in conjunction with the Bank of England.
It signals a shift in its approach to tackling the deficit – the Tories had pas previously committed to aggressively cutting public spending.
Liberal Democrat Shadow Chancellor Vince Cable says: “George Osborne and David Cameron seem to be at sixes and sevens on the crucial question of how the deficit should be addressed.
“The time to cut the deficit is when the private sector is ready to take the lead in growth and job creation. We are clearly not at that point yet.”