The TUV leader has written to the UK's National Crime Agency over a £1.5m donation made to Sinn Fein.
Sinn Fein received the windfall in the will of a party supporter who was born in England and living in Wales.
The gift was made by William E Hampton and paid in two instalments of £1 million and £500,000 in April and May.
The contribution is the largest donation given to a political party in Northern Ireland.
Mr Hampton, who was not married and had no children, left some money to friends and acquaintances, but the main beneficiary of the will was the Irish republican party.
It is understood that he spent some time living in Ireland and was a long-time supporter of the party before his death on January 11 2018 at his home in Pembrokeshire, Wales, at the age of 82.
However TUV leader Jim Allister has written to Lynn Owens, director general of the National Crimes Agency (NCA), over the matter.
Mr Allister wrote: "At or about the time when the will was made the Prime Minister, Tony Blair, was on record as describing Sinn Fein as being 'inextricably linked' with the IRA.
"In circumstances where decades of illegal activity, including bank robberies, accumulated ill-gotten gains for the IRA, I'd expect the NCA to be interested as to how such 'assets' might be laundered. Is the agency satisfied there is nothing untoward in respect of the aforesaid enrichment of Sinn Fein?"
Last week a Sinn Fein spokesman said: "Sinn Fein can confirm that it received a significant donation from a party supporter who passed away.
"We're obviously pleased that he has chosen to bequest this sum to the party and it's a positive boost to Sinn Fein in working towards Irish unity and towards our political objectives.
"We are in full compliance with the requirements of the Electoral Commission on all of this."
