The convention only has a month to come up with a constitution
The body drafting a new EU constitution is discussing a proposal for a directly elected president.
But the man leading the debate, former French President Valery Giscard d'Estaing, told the BBC the idea was "not realistic for now".
He said the convention on the future of Europe was discussing replacing the current rotating presidency of the European Council with a more stable president - but that he or she would not be elected by popular vote.
"This is not a proposal we will put in our constitution," he said on BBC Radio 4's Today programme.
He added that he could only imagine direct elections for the president of the Council - the body made up of governments of member states - in the distant future.
"Perhaps in 50 years," he said.
The convention's work is coming to a climax after a year of debate, with decisions now being made on the future division of power between different EU institutions.
Chaired by Valery Giscard d'Estaing
Holding year-long discussions
Aims to simplify treaties
Trying to decide balance of power between Brussels and governments
It must hand in a draft constitution to EU leaders next month.
But Mr Giscard d'Estaing underlined in his BBC interview that it will be up to EU member states whether to accept the draft.
He said an inter-governmental conference would take the final decision - and that the decision would have to be unanimous.
The EU's aim is to adopt the new constitution in time for the admission of 10 new members in May 2004.
Supporters of the idea of a more permanent presidency for the Council of Ministers say it would give the EU greater continuity and focus.
Germany, France and the UK are in favour, but a number of smaller states fear that the president would always come from one of the larger states - and that the power of the larger states would increase at their expense.
The Greek Foreign Minister, George Papandreou, has said the president would gain additional democratic legitimacy if he or she was elected.
British representatives on the convention disagree and would prefer an appointment to be decided by national governments.
Some convention members fear it might make a president too powerful.
Mr Giscard d'Estaing said that under the current system, few people in Europe even knew the name of the man who was in charge of the rotating presidency - currently the Greek Prime Minister Costas Simitis.