Conservative co-chairman Lord Maurice Saatchi has hinted a Tory government would cut taxes for the lowest paid.
Mr Howard is continuing the Tory policy of low taxes
The advertising supremo said it was a "chronic injustice" for those below the poverty line to pay income tax but added it was not his decision to make.
Lord Saatchi spoke to the Guardian in an interview to mark Michael Howard's first 100 days as Conservative leader.
Lord Heseltine, the former Conservative Deputy Prime Minister, said Mr Howard had made the party a "fighting force".
He told BBC Radio 4's Today programme: "The morale in the Tory party has been dramatically changed from one of absolute despair and
hopelessness to one in which it is now a fighting force anxious to be led.
"Michael Howard has shown the sophistication to rebalance the party in a way
that is designed to lead a united party and to lead it from the centre."
He said the government "almost certainly lied" on Iraq and had introduced stealth taxes depite promising not to increase tax.
Earlier Lord Saatchi told the Guardian the tax issue had irked him when he was Tory treasury spokesman.
He said: "I came across what I saw as a chronic injustice, which was that poor people pay more tax than rich people. That strikes me as not right."
The co-chairman has spoken before about taxing the poor, when he contributed to a 2001 report entitled Poor People! Stop Paying Tax.
At the time he called for the income tax threshold to be raised from the then figure of £4,385 to £10,000.
But in his interview with the Guardian he did not offer a concrete pledge of a cut for those on low incomes.
"It is a possibility. But like all policies in the manifesto, that will be Michael's decision."
Mr Howard has argued against high taxes, saying they have a negative effect on people.
In his recent "British Dream" speech, he said: "When taxes rise too high, they start to bring people low.
"There is a moral reason for government to take less from people in taxation.
"If people are highly taxed, they come to believe that their obligations to society and to one another are discharged just by handing money over to the government."
But Cabinet Office minister Douglas Alexander dismissed Lord Saatchi's comments on taxation.
He said: "Every time they open their mouths they
make another uncosted commitment. No one will believe the Tories' opportunistic
claims until they show how they will be paid for.
"This latest idea that the Tories have failed to provide a cost for would in
fact cost £30bn and the Tories have no idea how they would pay for it.
"And far from helping poorer families the Tories voted against the National
Minimum Wage and would scrap our tax credits, which are helping six million low
and middle income families."