Lloyds shares have jumped 65% since March
Lloyds Banking Group is prepared to pay a fee of close to £2.5bn to steer clear of the Government Asset Protection Scheme (GAPS), the BBC understands.
Lloyds believes it can survive without the GAPS and does not want the additional government influence which comes with the scheme.
The taxpayer already holds a 43% stake in the bank.
A decision on whether the arrangement goes ahead will be announced early next week, says the BBC's Nils Blythe.
The protection scheme, agreed in March, provides taxpayer guarantees against potential losses on some Lloyds assets.
The original idea was that the bank would pay for the guarantee by issuing new, non-voting shares that would give the taxpayer a majority stake in the troubled bank.
But Lloyds is currently talking to its major private sector shareholders about whether they will buy into a huge new share issue, in which the bank hopes to raise around £13bn - the biggest fund-raising of its kind to date, says BBC business correspondent Nils Blythe.
In addition, Lloyds will issue new bonds which will bring the total fund raising to more than £20bn.
With the extra cash raised by private shareholders, Lloyds feels it would then be in a position to decline additional government protection.
The £2.5bn fee would be in recognition of the guarantees provided by the GAPS since March.
Lloyds has been struggling since it bought HBOS last September. HBOS made a record loss in 2008 of almost £11bn.