The source said that Jose Manuel Barroso, the current European commission president, also stood a good chance of securing the post.
The official said: "Juncker and Barroso are at the moment the most credible people."
The new permanent EU president will prepare and chair the EU's summits of national leaders.
The post was created by the Lisbon Treaty which will take effect on January 1, 2009, if all 27 member states of the EU have ratified it by then.
The job is currently rotated between leaders of countries holding the EU's six-month presidency.
France takes over in July for the rest of 2008 and will be influential in negotiations on the new power-sharing arrangements at the bloc's institutions in Brussels.
Juncker, a centre-right politician who chairs monthly meetings of finance ministers of the 15-nation euro zone, is a seasoned negotiator who has been at the heart of every European deal since he came to power in 1995.
The French official said Britain was expected to oppose Juncker's candidacy because of his support for increased political integration among EU members.
However, Britain would not be able to block him on its own because the appointment of the new president requires the support of a qualified majority of EU countries rather than unanimity.
Anders Rasmussen, the Danish prime minister, has also been tipped to take the position.
The official said that it still remained open who was likely to be the EU's new foreign and security policy chief.
Javier Solana, the present EU's high representative for foreign and security policy, is a candidate for the enhanced new version of his post.
The drawback here was that many people would like to create the impression of a new page being turned, the source said.