But before such a thing can happen, the two countries would have to settle several long-simmering political spats, or at least choose to ignore them - a process that carries some heavy political and historical burdens.
In early June, Turhan Comez, a deputy in Turkey's ruling Justice and Development Party (AKP), visited Armenian deputy Hacat Sukyasian in Yerevan. This was the first visit by a Turkish parliamentarian to Armenia since Turkey sealed its borders with its eastern neighbour in 1993.
This closure came as a result of Armenia's conflict with Azerbaijan. Azeri defeat in the conflict led to Armenia occupying a land corridor between its frontiers and the Armenian enclave of Nagorno-Karabakh, which lies within Azeri territory. This occupation remains in place to this day.
Turkey has long supported its ethnic kin in Azerbaijan, and closed the border to pressure Armenia into resolving the conflict. Yet closing the frontier has had a major economic impact on both sides.
Armenia, small and landlocked in the Caucasus region, lost a large and valuable trading partner and a viable shipping route. Meanwhile, Turkey saw a collapse in commerce in its eastern provinces, which are now among its poorest.
At present, goods do circulate between the two countries, but largely via a more circuitous route, using connections through Georgia. This, however, is a far more costly business, both in terms of time and money. Direct flights do run between Yerevan and Istanbul, yet these are of minimal economic impact.
The co-chairman of the Turkish-Armenian Business Development Council (TABDC), Kaan Soyak, claimed back in February that according to official data, the volume of Armenian-Turkish goods in 2004 was a meagre $120m. This, he suggested, could triple should the border be reopened. TABDC also has ambitious plans ready to restore the Kars-Yerevan railway, should the border be reopened, turning the currently desolate eastern frontier into a major trade and transport corridor. This in turn would provide a boost to the local economy that might help reverse the trend towards depopulation on the Turkish side, as poorer rural dwellers head west for jobs in the big cities.
TABDC also has integration plans such as an online wholesale market for agricultural products grown in Armenia and eastern Turkey already set out.
Yet even with the obvious benefits for both sides, calls for an open border and trade between the two countries have had little impact in the past.
Armenia's foreign minister, Turkish and Armenian businessmen and Western diplomats have all expressed a preference for economic co-operation, and Yerevan has stated it is ready for an unconditional restoration of land links. However, Ankara has not been willing.
Yet, "Turkey's own economic interests are playing a role here," Nicolas Tavitian, TABDC's Brussels representative, says. "It is precisely because [the Turks have] much to win from the border reopening that they are perhaps seriously considering that possibility now."
As for Armenia, if the border were opened, Tavitian argues, citing World Bank statistics, "Armenia's exports would double in the short term and its GDP would increase by an estimated 30 to 40%."
However, while the economic arguments for reopening the frontier may have been clear for some time, the issue remains clouded by political and strategic concerns. Indeed, few expect any shift in Turkey's position as long as the Nagorno-Karabakh issue remains unresolved. While EU pressure may be on for Turkey to normalise its relations with its neighbours - indeed, this is a positive requirement of EU candidate Turkey in its accession process - and US pressure may be on as part of Washington's wider Central Asian strategy, Ankara remains largely pinned down by its Azeri commitments.
Meanwhile, the controversy over Armenian claims of a genocide committed by Ottoman Turks against them in 1915 also makes a resolution of disputes between Turkey and Armenia much more complex. At the same time, Ankara also accuses Yerevan of failing to satisfactorily renounce territorial claims on Turkey.
Yet Comez's visit, and generally positive reception, also indicates that there is strong pressure for change and reassessment building. Tickets through to Yerevan on the Kars railway may still be some way off, but they may not be entirely out of the question, either.