This discussion comes as the EU prepares to mark the 50th anniversary of the Treaty of Rome, the document that laid the foundation for the creation of the European Union.
Top strategists in the European Commission, the EU's executive arm, have decided the bloc should indefinitely postpone all questions concerning future enlargement.
They have warned countries such as Ukraine and Georgia to stop asking about expansion or risk an answer they do not want to hear. Both Kyiv and Tbilisi have taken the hint, with leaders of both countries now saying they are putting aside all talk of accession hopes for now.
But politicians in Brussels are increasingly aware that the stakes for the European Union itself are high.
'Never Say Never'
EU Enlargement Commissioner Olli Rehn spoke at a conference on March 19 and suggested the bloc is concerned about safeguarding the influence it has already won among its neighbors.
"We should never say 'never,' because if we did that, we would lose our political leverage," Rehn said. "We would lose our influence. And it's much better that we -- in the present sense and in the near future -- work on the basis of the European Neighborhood Policy."
Rehn appealed for an indefinite pause in the enlargement debate. Otherwise, he said, opponents could force the EU to draw "indelible lines" on the map, resulting in what he called a "Silver Curtain."
Graham Avery -- a former, but still influential, European Commission official -- explained some of the thinking behind Rehn's concerns. Avery said it would be wrong to force a decision about further enlargement now. He said skeptics within the EU could seize the opportunity to block expansion permanently, a scenario he described as "very damaging."
Speakers such as Avery noted that unanimous support doesn't even exist within the EU for countries that have already been promised membership -- from Croatia to Turkey.
Ambivalent About Expansion
On the eve of the EU's 50th anniversary celebrations on March 25, it is still unclear if enlargement will even get a mention in a declaration celebrating the bloc's achievements.
The Brussels conference -- organized by the European Policy Centre in Brussels in conjunction with the King Baudouin Foundation -- also served to launch a collection of essays by some of the EU's leading figures in which they attempt to predict the bloc's fortunes over the next 50 years.
Rehn attempted to lighten the mood by drawing a parallel with the United States, which he noted underwent one of its most sizable enlargements when the southwestern state of Texas entered the union in 1845.
"We can calculate that that makes something like 70 to 75 years since the foundation of the United States," Rehn said. "And by accident, 2033 is roughly 70 to 75 years since the foundation of the European Union. So, maybe a large eastern or southeastern European country is joining the European Union around those times."
Rehn could have been referring to either Ukraine or Turkey.