Reports in The Sun and The Times say that Mordaunt told the Cabinet that the 0.7 per cent aid target is 'unsustainable', that Dfid should help fund projects in other departments and that their ambitions should be less reliant on public money.
She has previously said the UK government: "will not invest when others should be putting their hands in their pockets".
Tory frontbencher Lord Bates, an international development minister, pointed out the pledge of 0.7 per cent was "enshrined in law", as he was pressed at Westminster for guarantees that there would be no move to "renege" on the target, which amounts to £13.9 billion.
Responding to the reports this week, Christine Allen, director of policy and public affairs at Christian Aid, told Premier: "We believe Britain's aid budget is a badge of honour worthy of pride and fierce defence.
"We are saddened that Penny Mordaunt is not eagerly fighting to maintain and even increase the 0.7% aid commitment given the rising number of people in dire need in Yemen, Syria, and many other emergencies around the world.
"When heads of government, faith leaders, celebrities and the British public themselves are recognising the dire need in our world, we expect our DFID Secretary to stand with them and celebrate Britain's determination to end poverty, and never bow to naysayers.
"To those who say Britain has many in need at home, we agree; but it is a false choice to help those here or those overseas. As the world's fifth richest country, we can do both".
Claire Godfrey, Head of Policy and Campaigns at Bond, a UK network of international development organisations - including Christian Aid, Tearfund, CAFOD and Care International UK - told Premier: "Any move to expand to the role of private sector investment in international development assistance must not undermine the very basic values of inclusive and sustainable development".
On the suggestion in The Times that more aid be spent by other government departments, Christine Allen from Christian Aid said:
"Britain's aid budget is not a cookie jar to be raided by other government departments. We know what aid is mandated for - relief of poverty - so where departments can't demonstrate that they are doing that effectively then they should not get aid money.
"To achieve maximum impact, aid should be focused on outcomes for the poorest, not on which department round the Cabinet gets a slice of the pie."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
