Membership in the EU's European Neighborhood Policy does not guarantee, or even address, entry to the bloc.
But Potocnik acknowledges that Georgia, Armenia, and Azerbaijan have all expressed an interest in eventually joining the European Union. Furthermore, he gives them reason to hope.
"Yes, I think one could relatively easily see that they are at a kind of crossroads. By all means, from the geographical point of view, from the historical point of view, from the cultural point of view, I think they have European roots. So, definitely, it is something where the answer would probably need to be positive," Potocnik says.
His mention of "European roots" has important implications. The current EU treaty says no country in Europe can be denied membership.
Still, he cautions, it will be a slow and uncertain process.
"One has to understand that what is happening in Europe is a very complicated process. On the one hand, you need [the] agreement between all European Union member states [on enlargement]. On the other hand, we're also finding, or focusing on, or seeing aspirations from other countries. So it's not something that could be done in one single big step. So clearly it is a step-by-step process and it is very difficult to envisage [at this moment] where things will go," Potocnik says.
So the South Caucasus countries must be patient. Their recent inclusion in the neighborhood program is itself a victory. Potocnik's advice is to first make the most of this opportunity.
"The EU at this stage could clearly not offer talks which would be connected to membership. But the neighborhood policy is clearly a major step forward. It's a step for increased cooperation and deeper integration in an economic sense. It offers [the countries] support in their own reforms which they would have anyway needed to do," Potocnik says.
Potocnik says Brussels does not look at the South Caucasus region as a single unit, and that the prospects of the three countries must be considered separately.
Potocnik points to Slovenia, which broke away from the former Yugoslavia to become its first -- and, so far, only -- EU member state. In the same way, he says, Brussels will judge Georgia, Armenia, and Azerbaijan according to their individual capabilities.
"I think on the one hand it is important that we encourage cooperation in the region. But on the other hand it's also important that we give them a chance [to] move according to their preparation, [internal] readiness, [in terms of] how far and how deep they would like to [go] in this cooperation and economic integration with the European Union," Potocnik says.
Potocnik refuses to rank Georgia, Armenia, and Azerbaijan according to development, saying only that all three will require "a lot" of effort to attain EU political and economic standards.
The European Commission has already begun work to identify major points of concern in the region and suggest ways to move forward.
Georgia is considered the clear front-runner. But Potocnik says what matters to the EU are practical, sustainable results.
"Clearly, successful first steps [were taken]. But on the other hand, it is also clear that the process of reform needs to be consolidated and further developed. The 'Rose Revolution' was clearly a step forward, and I think [Georgia] has huge, quite important potential for the future. But as I said before, its [potential] should be [put] into practice," Potocnik says.
The EU has concentrated its initial emergency support for Georgia on legal and judicial reforms, infrastructure, and regional conflicts.
The handling of South Ossetia by Georgia's relatively new government is seen as a crucial test. Potocnik says the EU would like a peaceful solution, and that any other approach would put the country's EU integration plans in danger.
There have been many recent EU missions to Georgia, as well as a donors conference resulting in pledges of $1 billion. But at the same time, Potocnik says he does not believe the bloc has neglected neighboring Armenia -- despite a lack of encouraging progress in the country's political system.
"What we notice [in Armenia is] the quite serious tension between government and the opposition, which refused to engage in any form of cooperation with the government. I believe that cooperation is quite important, and clearly democracy is still relatively weak. And the authorities will need to cooperate also with the opposition and I believe [this is quite] important for the functioning of democracy," Potocnik says.
Potocnik says the EU remains critical of Armenia's 2003 parliamentary elections and the subsequent crackdown on opposition demonstrations.
At the same time, the EU has offered Armenia 120 million euros ($149 million) to close down the Medzamor nuclear power plant and find alternative energy sources. In addition, the EU has offered to hold a donors conference and seek other international contributors to the project.
Potocnik says Brussels and Yerevan agree that Medzamor must be decommissioned for safety reasons, but that more money is needed to proceed.
Potocnik says that Azerbaijan shares many of the goals and values of its South Caucasus neighbors -- but is still hampered by the ongoing dispute with Armenia over Nagorno-Karabakh, a predominantly ethnic Armenian enclave on Azeri territory.
"I think it is one of the problems, which I felt they are somehow strongly kept [back] by -- the unsolved Nagorno-Karabakh problem. And [I feel] that their thoughts and their energies are quite a lot committed to the solution of that problem," Potocnik says.
After a recent visit to Brussels by Azerbaijani President Ilham Aliyev, EU diplomats told RFE/RL they were impressed by his dynamism. However, he appears to have made little headway when it comes to Nagorno-Karabakh.
Potocnik confirms the EU will not assume a mediating role in the conflict, preferring to leave it to the Minsk Group operating under the aegis of the Organization for Security and Cooperation in Europe (OSCE).
Azerbaijan is known to regard the Minsk Group with suspicion, fearing excessive Armenian influence over such members as France, Russia, and the United States.
Potocnik says OSCE mediation will be hampered unless Baku and Yerevan come to mutually acceptable terms.
Potocnik says Russia's role in the region is taking a "more constructive direction" -- particularly in Georgia, where Moscow played an active role in resolving the conflict in Ajara.
Potocnik says, however, that he feels Russia opposes greater EU involvement in the South Caucasus. He argues that the EU seeks stability and that this suits Russia's interests as well.
Potocnik also says he does not believe the EU and the United States are engaged in some form of strategic competition in the South Caucasus. He says that as a major global player, it is natural that the United States takes a keen interest in areas of conflict.