The Guardian said leaked Treasury documents suggested the measure could take effect in April 2016, benefiting more than 20,000 estates by 2020.
The measure will not be included in Wednesday's Budget but could feature in the party's election manifesto.
But the Lib Dems said the plans were a "cynical" pre-election move.
The Conservatives announced plans in 2007 to raise the inheritance tax threshold for passing on property and other assets to £1m. It was a pledge in the party's 2010 election.
However, the Lib Dems blocked any changes as part of their coalition agreement and inheritance tax thresholds have remained frozen since 2009.
Under current rules, no tax is paid on the first £325,000 of an estate's value. The allowance can also be transferred between married couples making it worth £650,000.
According to the Guardian, the Conservatives are considering plans for a new tax-free band worth £175,000 per person applying specifically to family homes or main residences passed on to a direct descendant of the deceased.
This, it claimed, would be transferrable between married couples making it worth a maximum of £350,000.
It could then be added to the existing inheritance tax threshold, meaning that in some circumstances properties worth up to £1m could escape inheritance tax altogether.
The plans, which would not be as generous as the Conservatives' 2010 inheritance tax policy, would reportedly cost about £1bn.
As part of the plans, allowances for estates worth more than £2m would be progressively withdrawn in relation to their value.
This "taper" scheme could result in about 2,000 estates paying up to £260,000 more inheritance tax by 2016-17, assuming the plans were introduced in 2016.
The paper, written by Treasury officials for the Conservative minister David Gauke, notes the scheme would be "very popular with the public and in the media" and would primarily benefit "high income and wealthier households".
"It will allow you to say you are exempting those with modest homes from inheritance tax, with up to £1m of assets exempted in certain circumstances," it states.
"This reflects the concern raised by the public about rising house prices increasingly leading to estates with a modest house particularly in London and the south east paying inheritance tax."
When he was shadow chancellor, George Osborne said the Conservatives would raise the Inheritance Tax threshold to £1m, the announcement coming in the autumn of 2007 amid speculation that the then prime minister Gordon Brown would call a snap election.
But the idea has not been seriously discussed since 2010.
Asked whether it was now being revived, Conservative business minister Matthew Hancock said "he did not know about that", merely saying that the idea had been "floated seven or eight years ago".
"That was in in our last manifesto just over five years ago," he told the BBC.
Mr Cable said many people in his west London constituency were concerned about inheritance tax and he understood the "human instinct" to pass on property to children.
But he said the plan sent a "very bad signal about the chancellor's priorities", which he said should be focused on reducing the tax burden on the lowest-paid.
"This is an old chestnut that is wheeled out before every election," he told the BBC.
Earlier this year, David Cameron said he would like to "go further" and take more families out of inheritance tax but warned about the cost of such a move.
But speaking on Tuesday, Mr Cameron said inheritance tax was "not something in the Budget" and dismissed suggestions the Lib Dems were standing in the way of his plans.
UKIP leader Nigel Farage told the BBC's Daily Politics he would abolish inheritance tax altogether, suggesting this "common sense, straight forward" move was the only way of helping people under-40 get on the property ladder in London.
The Treasury collected £3.4bn in inheritance tax in 2013-4, an 8.6% increase on the year before. However, yields remain below their peak of £3.8bn from 2007-8.
Nearly 16,000 estates were liable for inheritance tax in 2011-12 but this is projected to increase to 56,100 by the end of the next Parliament in 2020 as a result of house price inflation and the freeze in tax thresholds.
The proposed changes envisage that this number would fall to 34,300 by 2020.
The Conservatives have reportedly drawn up plans to allow some parents to leave homes worth up to £1m to their children without paying inheritance tax.