The Taoiseach Mr Ahern is sounding increasingly confident about getting agreement on an EU constitution before Ireland's EU presidency ends at the end of the month.
Mr Ahern, who is on a whistle-stop of EU countries ahead of the summit on June 17th and 18th in Brussels, said: "Hopefully, we can finish it in Brussels ... it is for us in a balanced way to try to find ... compromises that can get everybody on board."
"Over the weekend we have to sit down, and over next week, and bring the issues to finality," he said following a meeting with British Prime Minister Mr Tony Blair in London.
He also said that by the end of the week he - and he alone - would know his fellow EU leaders' thoughts on a new president of the European Commission, for which outgoing European Parliament President Mr Pat Cox is tipped.
Belgian leader Mr Guy Verhofstadt and Danish prime minister Mr Anders Fogh Rasmussen are front runners, although other reports favour Spain's Mr Javier Solana, now the EU's foreign policy chief.
But Mr Ahern said he would not divulge Mr Romano Prodi's successor until the summit. "My role in this, and I have done this confidentially with every head of state without telling any other head of state what everybody has told me, is to go through them all and then to make a report for the council," Mr Ahern said.
The Taoiseach indicated in the Dáil on Tuesday that vote weighting in the parliament and the make-up of the Commission remained the most problematic issue in getting agreement on the constitution.
He said his meetings with Britain, France and Germany were likely to play a central role in obtaining agreement as each country had significant "justice and home affairs" concerns.
However, the country's are also the EU's most populace and with Poland and Spain having opposed the draft constitution because they lose voting power, some sort of concession on that issue from the three EU superpowers could be in the offing.
But Poland is in a state of political turmoil at present and Mr Ahern indicated their position was not clear. "I am doing my best to figure out what Poland wants. It is having some difficulty but its position is no longer the same as that of Spain."
Diplomats say Ireland has circulated a new compromise proposal, said to involve an option for a group of states facing defeat on a vote to delay the decision and seek a threshold beyond simple majority.
Mr Ahern is meeting the leaders of the Netherlands and Belgium this afternoon and evening, and those of Luxembourg, Denmark and Germany tomorrow.
Additional reporting Reuters