The Taoiseach, Mr Ahern, and the North's First Minister-designate, Mr David Trimble, are to meet at Government Buildings in Dublin on Friday morning to discuss the issue of North-South bodies.
Senior political sources said that, despite the excellent relationship between the two leaders, it was uncertain whether Mr Trimble would be able to reach agreement with Mr Ahern on cross-Border bodies ahead of this weekend's Fianna Fail ardfheis.
There have been indications that the cross-Border issue is about to come to a head, with very strong feelings being expressed on the subject by senior figures in both the Ulster Unionist Party and the SDLP.
A meeting of senior unionists on this issue was held at the Armagh home of the UUP deputy leader, Mr John Taylor, on Saturday afternoon. The meeting took place against a background of reports that agreement with Dublin was imminent in this area.
But in what was described as an uncomfortable session on Saturday, trenchant views were expressed to Mr Trimble by leading party colleagues on the need to take a firm stance in this area, otherwise his leadership would be in jeopardy.
There is said to be anger at senior UUP level that Dublin was taking concessions on cross-Border matters for granted, and this has caused a chill in relations between the UUP and civil servants from the Republic.
UUP sources said officials from Dublin were present for roundtable talks at Stormont yesterday, "but they didn't seem to engage very much".
Although UUP leaders are said to be willing to accept cross-Border bodies in non-controversial areas such as inland waterways, sources said they could not "buy into" North-South institutions on tourism at this stage, and that accepting a joint organisation to promote industrial development would amount to political suicide.
Relations between the UUP and SDLP are said to be at a low ebb, with a meeting between the two parties last week described as "the worst they have ever had".
Political insiders said there was no crisis in the peace process but that the potential existed for a full-blown if somewhat artificial crisis to develop, probably over prisoners.
Mr Trimble is expected to address the North-South issues in separate speeches to the Association of European Journalists and the Irish Association on Friday. He will also reiterate his party's strong stance on decommissioning. However, political sources say that, privately, central elements in the UUP leadership "couldn't give tuppence" about the issue, but it had to be highlighted because of internal unionist politics.
Senior UUP members such as Mr Trimble and Mr Taylor have begun to highlight the issue of prisoner releases, but the UUP is conscious of the fact that any attempt to block prisoner releases would alienate the Progressive Unionist Party, the political wing of the Ulster Volunteer Force.
The UUP leadership will not lightly jeopardise the support it receives in the Assembly from the two PUP representatives, Mr Billy Hutchinson and Mr David Ervine.