There is a growing belief among EU leaders that the EU constitutional treaty can be agreed before the end of Ireland's EU presidency, with consideration now being given to trying to do a deal as early as next month.
The Irish presidency remains cautious about the prospects, with the Taoiseach, Mr Ahern, starting a final round of pre-summit discussions in Paris today with French President Mr Jacques Chirac.
However the Spanish prime minister-elect, Mr José Luis Rodriguez Zapatero, yesterday added to the optimism, saying "the European constitution can be approved in the short term if we regain political cohesion".
Mr Ahern is expected to circulate a report to his fellow EU leaders on Wednesday giving his assessment of whether a deal can be done.
There will then be a discussion of this on Thursday night at the European Council meeting in Brussels, following which the council is to decide whether to reconvene the Inter Governmental Conference to finalise the constitution.
Speculation now focuses on whether they will choose the most ambitious option of seeking a deal before the European parliament election campaign begins, or whether they will wait until after the June 11th elections. The former would mean trying to agree everything before the end of April, with the latter involving an attempt to strike a deal before the Irish presidency ends on June 30th.
Should this week's European Council meeting agree to try for a deal, EU foreign ministers would first meet one or more times in IGC format before sending a draft deal for final approval by EU heads of state and government.
Choosing the more ambitious timetable would mean that a special European Council meeting would be called for April if a deal can be done.
The Minister for Foreign Affairs, Mr Cowen, will chair a foreign ministers' discussion of the outstanding issues in Brussels today, as Mr Ahern meets Mr Chirac in Paris.
Tomorrow, the Taoiseach may discuss the issue briefly with Mr Blair during a meeting at Hillsborough devoted mainly to the peace process in the North. Last week he spoke to Mr Zapatero by phone.
The Taoiseach is also awaiting the outcome of a meeting in Warsaw on Tuesday between German Chancellor Mr Gerhard Schröder and Polish Prime Minister Mr Leszek Miller. It is hoped that this encounter will bring a clearer view of the level of willingness in the Polish government to compromise and accept the so-called "double majority" voting system.
The Taoiseach said yesterday that he would be producing "a short report containing a summary account of the work done to date and our overall assessment of the state of play".
While agreement is dependent on the positions taken by other states, a successful deal would be a substantial achievement for Mr Ahern whose handling of the issue over the past two months has been widely praised by diplomats from other member states.