The government could announce an inquiry into the 1989 murder of Catholic solicitor Pat Finucane within days, Sinn Fein has said.
Pat Finucane was shot dead by loyalist paramilitaries
It is understood discussions took place on Saturday between the prime minister's chief of staff, Jonathan Powell, and Mr Finucane's widow Geraldine.
Loyalist Ken Barrett was sentenced at Belfast Crown Court to life for Mr Finucane's murder on Thursday.
The government handed its proposal for an inquiry to Sinn Fein the same day.
Sinn Fein President Gerry Adams said his party supported the Finucane family's demand for a full public inquiry and had suggested the government speak to the family.
There are concerns about the terms of reference for the inquiry - concerns which fall into the category of national security.
On Sunday, the SDLP's spokesman on policing said an inquiry would have to fulfil the recommendations of retired Canadian Judge Peter Cory.
Alex Attwood warned that any inquiry must be conducted in public.
"There must not be devices created whereby those who have something to account for are given protection under the law," he said.
Judge Peter Cory was appointed by the British and Irish governments to examine allegations of collusion surrounding some of the most controversial killings of the Troubles in Northern Ireland.
He recommended a public inquiry into Mr Finucane's death.
Mr Finucane, 39, was shot dead by the loyalist Ulster Defence Association.
The killing was one of the most controversial of the 30 years of the Troubles in Northern Ireland, mainly because of the allegations of collusion between loyalist paramilitaries and members of the security forces.
First person charged
Ken Barrett admitted the killing of Mr Finucane in the kitchen of his family home in north Belfast in February 1989.
However, the 41-year-old could be freed within months under the terms of the Good Friday Agreement.
Barrett entered the guilty plea at the beginning of his trial in the Crown Court in Belfast on Monday, having denied the murder at previous hearings.
He was the first person to be charged with the solicitor's murder.
On Thursday, Mr Justice Weir described the "cruel and callous" murder as a "terrorist killing carefully planned and mercilessly executed".
The Finucane family said they were not particularly interested in convictions, and that Barrett's guilty plea served to conceal the truth that could only emerge at a public inquiry.