The NHS in England faces a funding gap of up to Â£2bn, about 2% of its budget, for the next financial year, the BBC understands.
Senior health sources told the BBC growing costs would outstrip the money the NHS received from April 2015.
Health Secretary Jeremy Hunt is involved in Whitehall talks on how to plug the gap.
The Department of Health said it was “confident” it would “make the savings necessary to meet rising demand”.
The NHS’s budget in England for 2015 has been set at about Â£100bn.
The NHS has experienced a prolonged budget freeze as part of the government’s plan to reduce the UK deficit.
Its budget has been protected from cuts which have affected most other government departments, but spending has risen only at the rate of inflation.
Factors including population growth have led to increasing demand on NHS services and higher NHS pension costs have added to the financial pressure.
In a statement, the Department of Health said: “The NHS is on track to make Â£20bn savings this parliament and we are confident that it will continue to make the savings necessary to meet rising demand.”
But some health chiefs told the BBC the sums for the financial year beginning next April did not add up.
Nearest tube: Elephant & Castle underground station (Northern and Bakerloo lines).
Nearest Railway Station: Elephant & Castle
Buses from Elephant and Castle: ask bus driver for Burgess Park. Bus numbers: 12, 171, 148, 176, 68, 484, 42, 40, 45