An offer of "qualified immunity" has been made by the Director of Public Prosecutions to the man involved in allegations over a cash payment to the Minister for Foreign Affairs, Mr Burke.
A senior garda has told the man that he will have "qualified immunity" from prosecution if he signs a statement detailing his allegations. This would allow a formal Garda investigation to proceed.
Supt John McElligott of Garda Headquarters has made the offer to Mr James Gogarty, a former building firm executive who handed over cash to Mr Burke in the politician's Dublin home in 1989.
Mr Burke said last week that he received £30,000 as an "unsolicited political contribution" from Mr Gogarty. He denied receiving more cash from another director of a building company who was present.
Mr Gogarty has given a separate version of events to the Garda. However, he has so far not backed up his verbal allegations with a signed statement.
The former building company executive has indicated to investigating officers that he fears prosecution if he signs a statement which might implicate him in any offences.
Over the past three weeks the DPP has given the go-ahead for Mr Gogarty to be offered "qualified immunity" relating to a specified range of offences which might emerge during the investigation.
Supt McElligott, who has been investigating Mr Gogarty's allegations, has repeatedly made the offer to Mr Gogarty, but so far no statement has been signed.
Mr Burke admitted on Thursday that he received £30,000 from Mr Gogarty during a meeting at the Minister's home during the 1989 general election campaign.
He said he received the payment "in good faith" from Mr Gogarty, who represented Joseph Murphy Structural Engineers Ltd. He denied having received a sum of £80,000, or having received £40,000 from Bovale Developments Ltd or its director, Mr Michael Bailey, who was also at the meeting.
Fianna Fail sources have said £10,000 of the £30,000 was paid by Mr Burke into central party funds, but Mr Burke's statement of last Thursday did not mention this.
It is understood that the Garda has been reluctant to pursue the investigation on the basis of Mr Gogarty's verbal allegations alone. However, if Mr Gogarty signs a statement the Garda will then be in a position to revive the investigation, including formal questioning of potential witnesses.
No Government, Foreign Affairs or Fianna Fail spokesperson could confirm yesterday that the Minister personally telephoned the Sunday Independent last Saturday night to say he planned to take legal action over an article due to appear yesterday in the Sunday Business Post.
Mr Burke was not available to comment and spokespersons for the party, the Department and the Government said they knew nothing about the call.