KSF's portfolio was originally put on the block in November 2008, a month after it went into administration.
Reportedly, KSF had lent millions of pounds to high profile individuals and property developers. The bank's £1bn property book, which includes a £160m loan against The Shard tower, which is expected to open in time for the 2012 London Olympics, is said to be one of the attractive assets to potential investors.
A spokesman of Ernst & Young said: "The administrators objective is to realise Kaupthing's business and assets for the benefit of the creditors and therefore they review the range of options available to them on a regular basis."
In December 2009, Serious Fraud Office, the UK body that investigates and prosecutes serious and complex fraud, had launched a formal investigation into suspected fraud at Kaupthing prior to its collapse at the height of the financial crisis.
The SFO is particularly interested in efforts made to attract UK investors to the purportedly high yield deposit account, Kaupthing Edge. The investigation will seek to identify whether misrepresentations or false representations were communicated by the bank in its push to attract UK investors.