Amid rising criticism of the plans, Foreign Secretary William Hague told Sky News: "Finding a solution that takes account of the concerns that have been expressed is something the Prime Minister and the Chancellor are open to."
Among those raising concerns were the head of Marie Curie Cancer Care, the co-founder of the Body Shop and three daughters of Lord (David) Sainsbury, the Labour peer.
Nearly 50 donors writing in the Sunday Telegraph said the changes would be a "brake on philanthropy".
Amid mounting criticism, the paper reports ministers are now looking at changes to the plans, which are aimed at closing a tax avoidance loophole.
Higher-rate taxpayers donating to a charity can currently reclaim more than half of the tax, in some cases reducing their tax bill to nothing.
But under the plans announced in the Budget, from next April the relief would be limited to £50,000 a year, or 25% of the giver's income.
Charities fear that this will cause a large drop in donations, and some may choose to donate nothing.
Sir Menzies Campbell MP, who is chancellor of the University of St Andrews, told Sky News' Murnaghan programme there is "anxiety" among charities about how they would secure funds under the new plans.
Speaking days after the university received a donation of £1m, he said: "There doesn't appear to have been any consultation about (the new rules)."
And he added: "The consequences of the increases... have got to be regarded with great seriousness."
Philip Spedding, head of the Prince of Wales' arts philanthropy charity, told the Sunday Telegraph the plans were "astonishing".
In the donors' letter, they said: "The proposal in the Budget to cap charity tax reliefs is a brake on philanthropy that may defer future donors.
"It is confusing and dispiriting, and we urge the Prime Minister and Chancellor to think again."
They said their gifts were not just for tax relief, "although it may substantially increase our donations".
Conservative MPs and Liberal Democrat Business Secretary Vince Cable have previously expressed their unhappiness with the proposals.
The Treasury has insisted the plan will go ahead.
It said: "The Government does not think that it is right that very wealthy individuals can use tax reliefs without limit to reduce their tax bills to close to zero, often year after year.
"We support charitable giving and the vast majority of donations will be completely unaffected."