In the lead-up to Kaupthing's bankruptcy in October 2008, it has been suggested that certain traders used around â¬500 million ($598 million) from the bank's own funds to make credit derivative swaps in an attempt to restore confidence in the firm.
During the earlier part of that year, the price for insuring Kaupthing bonds against the possibility of the bank going bust had been rising sharply because of fears about the company's solvency.
It is alleged that executives at the bank, who wished to reverse these increases, extended loans to investment vehicles owned by trusted clients to conduct credit default swaps on the bonds.
Deutsche Bank, which is said to have been playing an advisory role to Kaupthing during this period, is being targeted by the SFO over allegations it may have improperly helped to push through such trades, reports the Guardian.
Investigators are now looking into the correspondence between Deutsche Bank and Kaupthing's senior staff members at the time, including executive chairman Sigurdur Einarsson and chief executive Hreidar Mar Sigurdsson.
Last year, Mr Einarsson stated that Deutsche Bank had originally been behind the idea.
"On a proposal from Deutsche Bank it was decided to put to the test what would happen if the bank itself would start buying these credit default swaps," he said.
"[We got] clients we trusted well and had long-standing relations with based on trust and loyalty to engage in these transactions on behalf of the bank."
He added that the transactions were made "fully in accordance with laws and regulations".
A spokesman for Deutsche Bank said the firm was co-operating with the authorities on the investigation.
Last month, Mr Sigurdsson was arrested on a variety of charges, including embezzlement, market manipulation and falsifying documents.
By Claire Archer