Italian Prime Minister Silvio Berlusconi has said he will replace his controversial nominee to the European Commission, Rocco Buttiglione.
The EU constitution was signed against a backdrop of crisis
Mr Buttiglione has been at the centre of a storm over his comments on homosexuality and women.
Incoming Commission President Jose Manuel Barroso withdrew his entire team amid fears it would be vetoed by the European Parliament on Wednesday.
The furore overshadowed the signing of the EU constitution on Friday.
EU leaders took it in turn to sign the text in a lavish ceremony in Rome - in the same room where the Treaty of Rome was signed to establish the EU in 1957.
But as the event progressed, Mr Barroso was holding hurried talks with EU leaders to seek support for his planned changes to the commission.
Mr Berlusconi told reporters on Friday that Mr Buttiglione would most likely be replaced as Italy's nominee to the new commission, but remain a minister in the Italian government.
"It is useless to deny that this is the most likely outcome," Mr Berlusconi said.
Mr Berlusconi has called a news conference on Saturday morning where it is expected the decision will be formally announced.
The Italian premier gave no indication of whom he would propose as a candidate to replace Mr Buttiglione.
The BBC's David Willey in Rome says one name that has been frequently mentioned is Mario Monti, who has already served in Brussels as Competition Commissioner.
Mr Monti, a former economics professor, is widely respected by his peers as an impartial and very competent candidate, our correspondent says.
Mr Buttiglione, a close friend of the Pope, caused outrage when he said homosexuality was a sin and single mothers were not very good people.
Opposition to Mr Buttiglione gathered pace, and on Wednesday Mr Barroso was forced at the last minute to withdraw his team amid fears it would face an unprecedented veto from the European Parliament.
On Friday, EU leaders gathered to sign the new constitution in the Renaissance splendour of the Campidoglio, the city hall inspired by Michelangelo in the centre of Rome's historic district.
As music played in the background, each leader and foreign minister stepped up in alphabetical country order to sign a giant tome. They shook hands with each other, with a beaming Mr Berlusconi, and then progressed along a line of dignitaries.
Europe's leaders put on a united front despite the threat of crisis, the BBC's Tamsin Smith reports.
And the celebration of a treaty designed to bring Europe closer to the people took place behind a formidable police cordon, she says.
Up to 7,000 police and security forces were on Rome's streets to protect EU leaders, while a squadron of F-16 fighters enforced a no-fly zone over the city centre.
Despite the signing of the constitution, member nations still have to ratify the document individually before it comes into effect - either by referendum or parliamentary vote.
A number of countries, including France and the UK, will hold public votes, with the first vote expected to take place in Spain in February.
The constitution intends to make the union function more smoothly.
But plans for an EU president overseeing the co-operation between member states, and a change in the voting system, have caused divisions in EU states.
The new treaty also sees a big expansion in the number of policy areas where countries will lose their national veto, and includes the creation of a foreign minister's post.