The account, thought to have contained around Â£7m, was to be used to facilitate payments to people involved in arranging the sale.
The bank account was controlled by Ian Coulter, a former partner in Belfast law firm Tughans.
He left the company in January.
It was to be used for payments to so-called fixers and influencers behind the sale of  Nama's Northern Ireland property portfolio.
Last week, Independent TD (Irish MP) Mick Wallace claimed in the Irish parliament that the money was earmarked for a politician in Northern Ireland.
Tughans has said the money was "diverted" into the account without the knowledge of other senior staff.
It said the payment was retrieved and Mr Coulter left the company at the start of the year.
In a statement on Wednesday, the PSNI said it will launch a criminal inquiry into concerns raised over the Nama sale and the claims made by Mr Wallace.
Assistant Chief Constable Will Kerr said the PSNI believed there was sufficient concern in relation to potential criminal activity surrounding the property deal to instigate an investigation.
He said the police were engaging with a number of other national and international law enforcement partners to consider how best to take it forward.
It is understood those other law enforcement organisations include the National Crime Agency - referred to as the British FBI.
In a statement on Wednesday, a DUP spokesperson said: "This is a welcome announcement and the appropriate step to deal with the serious allegations which have been made.
"Indeed, the First Minister Peter Robinson called for such action by the authorities last week noting that accusations of criminal behaviour tarnish politics and should be fully investigated."
Sinn FÃ©in's Martin McGuinness said it may be necessary to have a full judicial inquiry into the Nama sale.
The Law Society, which is responsible for regulating the activities of solicitors in Northern Ireland, has been investigating the circumstances of Mr Coulter's departure from Tughans since January.
On Tuesday, it said it will co-operate fully with any police investigation.
The police are to launch an investigation into the sale of Nama's property portfolio in Northern Ireland, and claims about money contained in an Isle of Man bank account.