The individuals named in Tchenguiz's claim are Stephen John Akers, Hossein Hamedani and Johannes Runar Johannsson. Akers, Hamedani are both partners at Grant Thornton, while Johannsson is an Icelandic lawyer.
Read MoreVincent Tchenguizsettles after botched fraud probe
Akers, Hamedani, Johannsson were not immediately available for comment. A spokeswoman for Grant Thornton said the firm needed to read the claim before commenting. Kaupthing was not immediately available for comment.
After the SFO subsequently dropped its investigation, Vincent and his brother Robert blamed "external influences" for the events that led to their arrest and said they would pursue those they said were responsible and liable for the damage caused.
Read MoreProperty Tycoon Tchenguiz 'Will Recover' From Fraud Probe
Vincent and Robert had sued the SFO over their arrests in March 2011 in a case linked to the 2008 collapse of Kaupthing.
The Iranian-born brothers argued that the publicity surrounding the investigation inflicted lasting damage on their reputations and businesses.
They reached a joint 4.5 million pound out-of-court settlement with the SFO this year, excluding hefty legal costs. This averted a civil trial and further public airing of the SFO's handling of a case.