The proposal to cut sentences by a half for those criminals who admit their guilt at an early stage are "as good as scrapped" following a public backlash, according to political editor Nick Robinson.
But the change should not be seen as a blow for Justice Secretary Ken Clarke, as the change of was outlined in the spending review last October as a means to save money.
"It is the government that has a problem now, not Ken Clarke. The government has to decide where do you find £130m?" he said.
Former Conservative leader Lord Howard said he hoped the reports of the changes being scrapped were right, but denied that the government was in retreat.
"I'm not sure that retreat is quite the right word," he told the programme, arguing that a "listening government" had responded to the views of the public.
The move would have been "an affront to many victims of crime" and would not have had the desired effect.
And he denied that the shift meant that the right wing of the party had triumphed over the liberal wing.
"I don't think it's got anything to do with wings of parties," he said.
"Ken [Clarke] is an old friend of mine, and he's a very robust character. He's encountered many greater difficulties than this during the course of his political career."
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