The Icelandic investigation relates to the purchase of a 5.01 per cent stake worth around $244 million in Kaupthing by Sheik Mohammed Bin Khalifa al-Thani, a Qatari royal, in mid-September 2008.
But the deal had been financed using loans from Kaupthing itself, a fact Mr Einarsson did not disclose at the time, reports the Observer.
Although this loan was covered by personal guarantees from Sheik Mohammed, investigators are looking into a second loan given to one of his companies that allowed him to clear almost all of his personal liability.
The loan was given without any collateral or guarantees and eight other people are now believed to be under investigation over what happened.
One month after the announcement of the Sheik's purchase of the stake, Kaupthing went bust, owing bondholders billions.
Mr Einarsson has denied the charges of market manipulation and said the second loan was for a separate investment that did not go through because of the bank's collapse.
Lead investigator Olafur Hauksson refused to confirm the Observer's report and told the Times that the information Mr Einarsson was a suspect had not come from his department.
By Tony Aynsley