Lib Dem Business Secretary Vince Cable has led calls for this in cabinet but David Cameron and Nick Clegg have previously ruled out funding such a move by increased borrowing.
The idea of moving the responsibility of the BSkyB bid from Business Secretary Vince Cable to Mr Hunt was suggested by Cabinet Secretary Jeremy Heywood, Mr Cameron said, following a series of meetings with Deputy Prime Minister Nick Clegg and Downing Street staff.
But Lib Dem peer Lord Oakeshott said his party's Business Secretary Vince Cable had "given a very serious warning last Monday in the cabinet against elevating these financial regulation points into a make or break deal".