The Liberal Democrat peer Baroness Barker put forward an amendment to the Children Bill to allow the Government to set a minimum allowance.
The Education spokeswoman and government whip Baroness Andrews said she could not accept the amendment, but expressed her sympathy for the cause and revealed that ministers were considering the "complex issues" of such a scheme.
BAAF Adoption & Fostering chief executive Felicity Collier was "optimistic" that there would be some movement from the Government, because "we have won a lot of hearts and minds".
"I had a very productive meeting with (junior education minister) Baroness Ashton, and she listened very carefully to the arguments," she added.
Vicky Swain, campaign manager at the Fostering Network, said: "It is a simple principle that foster carers ought to be paid the full cost of looking after children."
Speaking in debate during the Lords committee stage of the Children Bill, Baroness Andrews said: "We're well aware of the current campaign to introduce a standard national allowance for foster carers.
This raises complex issues and we are giving them careful consideration.
"I have listened very closely to the arguments of noble Lords and we will reflect on them. We will also think further on the important issues being raised by those who are campaigning on these issues."
But Baroness Andrews rejected outright another amendment to set up a private fostering registration scheme immediately. The Children Bill gives ministers the power to do so within four years, but only if plans to strengthen local authority notification arrangements do not work out.
