The bank is also keen to shrink its involvement in the asset protection scheme below the agreed £260bn.
According to the Daily Telegraph, Lloyds is looking to launch a rights issue of up to £10bn.
The paper says the FSA is stress-testing this plan as well as proposals to sell Scottish Widows, Clerical Medical and Lloyds’ stake in St James’s Place.
Lloyds submitted formal proposals to the Treasury this week and the Treasury has passed these on to the FSA.
Lloyds wants to reduce its participation in the APS because it considers the fee too expensive and fears it will hand the taxpayer too large a stake, according to the Telegraph.