The move would propel the continent's second-largest country into the orbit of the 28-nation European Union rather than Vladimir Putin's Kremlin.
Taken to its logical conclusion, Ukraine's farm fields, mines and factories, which are now mainly oriented toward the Russian market, could eventually chiefly produce for the EU—the world's largest single economic bloc, extending as far west as the British Isles.
Its capital city of Kiev, known as the mother of Russia's cities, could one day have denser links with Rome, Paris and London than with St. Petersburg, Smolensk or Moscow.
The country's military, one of Europe's largest, might join the U.S.-led NATO alliance.
Ukraine "has the potential to really boost the EU's engine in a way that no other new member could - with the exception of Turkey," said Amanda Paul, a policy analyst at the European Policy Center, a Brussels think tank. "Ukraine's new generation of youth are well educated and therefore needed by Europe, which has an aging population."
Incorporating Ukraine and its 46 million people into the EU would make the bloc a player in Central Asia and the Caucasus, put EU-Russian relations on a much closer footing and bring about an internal EU power shift that would strengthen the influence of Poland and other Eastern European countries at the expense of southern Europe, said Jan Techau, director of Carnegie Europe, another think tank.
"It's a pretty big strategic shift we're talking about," Techau said.
With the disappearance of Ukrainian President Viktor Yanukovych, chances appear to have brightened for Ukraine to sign the formal association agreement with the EU that he spurned in November in favor of a bailout loan from Russia a month later.
That EU deal, in the long run, could prove a bonanza for the resource-rich republic that was one of the former Soviet Union's industrial dynamos.
In the short term, however, it would be excruciatingly painful for many sectors of Ukraine's economy and would commit the EU and other international organizations like the International Monetary Fund to spending billions in aid.
Present-day Ukraine, Techau said, is a "basket case economically."
Closing the EU deal appears much more possible than it did a week ago when Yanukovych was in charge. The Ukrainian parliament speaker who has assumed presidential powers, Oleksandr Turchinov, has said one of his priorities will be "returning to the path of European integration."
Independent experts, though, caution that path is full of challenges.
Geoffrey Pridham, an emeritus professor who studies post-communist democratization at Bristol University in Britain, said three factors —Ukraine's dire economic situation, the stirrings of pro-Russian separatist sentiment in the east of the country, and Kremlin meddling—could derail any effort to bring Ukraine closer to the EU.
"It really depends on what Russia decides to do," said Kataryna Wolczuk, associate professor of international studies at the University of Birmingham. "We haven't heard the last word from Russia."
Some European officials have been trying to tamp down expectations of what their side can afford to accomplish. Asked about the chances of Ukraine joining the EU, German Chancellor Angela Merkel's spokesman, Steffen Seibert, told reporters in Berlin on Monday that "we have always said that the conclusion of an association agreement could start a process from which Ukraine might profit in other ways.
"At the same time, we shouldn't raise expectations and hopes that can't be fulfilled," Seibert said.
Were it to join the EU's ranks one day, Ukraine would have the largest European land area of any member state and be one of the bloc's most populous countries. It would also be a relative pauper and soak up resources at a time when other member nations are struggling to restart their own economies.
According to the World Bank, the average per capita income in 2012 was $41,863 in Germany and $39,772 in France, compared to just $3,867 in Ukraine.
The EU's top diplomat, Catherine Ashton, went to Kiev this week to feel out the situation. EU officials say there can be a win-win outcome that doesn't injure Moscow's interests.
"The European Union has everything to gain from increased trade and investment ties between Russia and Ukraine," spokesman OIivier Bailly said, adding the bloc was hopeful that Russia will join with it in playing a "constructive and supporting role" that benefits Ukraine.
Ewald Boehlke at the German Council on Foreign Relations is hopeful that Washington, its European allies and Moscow can find common ground.
"The Ukrainian state must be a stable state and that means to work together between the EU, Russia and the United States; otherwise we will lose control of society in Ukraine," Boehlke said.
However, other experts told The Associated Press the EU needs to ramp up its game.
Georges Mink—a specialist in central and eastern Europe at France's National Center for Scientific Research and the College of Europe in Natolin, Poland—said Europe must act to help transform Ukraine into "a prosperous country that is free to choose its orientation."
The EU "has an interest in avoiding on its borders an unstable country, a wrecked country, one that could fall prey to imperial designs," Mink said. "There must be an all-out effort to help the transition to a new Ukraine take off."
Paul, who has been following events in Ukraine for a decade, said for the westward-facing scenario to become a reality, the EU must get tougher with Putin.
"The ultimate question is, is EU ready to tackle Russia? They need to stop being so cowardly," Paul said. She said she believes the high hopes many Ukrainians are vesting in the European Union may ultimately be dashed.
Juergen Baetz in Brussels, Lori Hinnant in Paris, David Rising and Frank Jordans in Berlin, Raphael Satter in London and Alison Mutler in Bucharest contributed.