"Clearly there are talks going on, but it is very early days," the source said on Friday.
The Asset Protection Agency (APA) – which insures £230bn of risky assets held by RBS – was set up in 2009.
RBS, the Treasury and the APA declined to comment.
Hopes that RBS could leave the scheme earlier than planned lifted shares in the bank, which is 80-percent owned by the state after a taxpayer bailout during the credit crisis, 5.1 per cent to 44.34 pence by 10:40 a.m making it the best-performing stock on the FTSE 100 index.
"We see this possibility as positive for RBS in terms of sentiment and in terms of reduced government asset protection scheme insurance payments," brokerage Oriel Securities said in a research note. Oriel kept a "buy" rating on RBS shares.
RBS chief executive Stephen Hester had said the earliest exit from the scheme would be 2012.
The source said on Friday uncertainty remained over the timing of an early RBS exit, and the scheme's insurance cover on RBS's riskiest "toxic" assets remained vital.
"These markets are still very uncertain and you cannot be sure about just how toxic some of those assets are."
As of March 31 last year, £231bn of risky RBS assets were covered by the scheme, for which RBS pays a fee.
The cover for those assets operates like a conventional insurance policy. If RBS's assets fall in value the bank will absorb the first £60bn of losses.
Further losses are shared by RBS and the government, with RBS taking ten per cent of the loss and the government 90 per cent.