Sinn Féin and the DUP are insistent they are both prepared to make a deal at talks in Leeds Castle in Kent that would lead to the restoration of devolution.
The DUP's Mr Peter Robinson said there was the "tantalising" possibility of agreement, while his colleague, Assembly member Mr Gregory Campbell, said that the DUP was "up for a deal".
British and Irish government sources also say that while there are major obstacles to be surmounted, the parties were approaching the negotiations in a positive frame of mind.
"Things are going in the right direction," said a talks' insider.
The Sinn Féin president, Mr Gerry Adams, and the DUP deputy leader, Mr Peter Robinson, respectively at a press conference in Belfast yesterday and in an article in this edition of The Irish Times, said agreement was possible in the talks scheduled to conclude on Saturday at lunchtime.
Mr Adams said he could not absolutely predict how the negotiations would proceed, but he wanted to see a comprehensive deal.
"I can't call it. All I know is that if it were down to Sinn Féin it would have been sorted last October, last May, the year before, the year before, the year before. So we are there to try to make it work," he said.
Right up to the beginning of the talks senior British and Irish officials are in continuing talks with the main negotiators for Sinn Féin and the DUP to try to agree an agenda that would focus on the primary issues: ending paramilitarism, ensuring unionists will share power, policing, and also trying to find agreement over possible amendments to elements of the Belfast Agreement.
A key associate of Mr Adams stressed yesterday that resolving