Russia does export significant volumes of oil and gas to Asia, though much less than it sends to Europe. Asian buyers are much less likely to participate in sanctions imposed over Russian actions in the Ukraine.

Russia can significantly increase sales to Asia, though there are serious infrastructure constraints and the shift will take time... just as it will take time for any prospective US exports to have any impact on European supply issues.

Some discussion of the question of the US supplying gas to Europe here:

http://www.platts.com/latest-news/na...ssian-21392003

http://www.miamiherald.com/2014/03/2...s-natural.html

From second citation above:

Europe relies on Russia for nearly a third of its natural gas, a fact that Russian President Vladimir Putin uses to his political advantage. But it is questionable how much increased American exports could hurt Putin, since most are destined for Asia, not Europe, and are years from reality.

The global consulting firm IHS Energy said in a new report that U.S. exports of liquefied natural gas, known as LNG, “can have no real” impact on the Ukrainian crisis, a conclusion that echoes other analysts.

“Much attention has been focused in recent weeks on the potential for U.S. exports of LNG to help Europe offset its dependence on Russian gas,” the report said. “Although the United States is currently on track to become one of the world’s three major LNG exporters by 2020–22, IHS Energy expects the ultimate impact on European gas supply to be limited.”

Natural gas prices are far higher in Asia than Europe, so companies are more interested in exporting to the hungry Asian market. The European countries most dependent on Russian energy don’t even have terminals for receiving U.S. liquefied natural gas and receive their energy by pipeline.
I get the feeling that much of the talk of US gas addressing Europe's dependence is intended less to influence the situation in the Ukraine than to influence domestic debate on fracking and on the Keystone pipeline.

It is worth noting that right now the US has no LNG export capacity at all, something the Lituanians at least don't seem to realize:

http://www.bbc.co.uk/news/business-26724081

The terminal under construction at Sabine Pass, TX could export in 2015 or 2016, Freeport TX by 2017. Much of their output is already committed to Asian buyers. Most other proposed terminals are in the approval or early construction phases. US gas is not going to come rushing to Europe's rescue. There will be a displacement effect, as US imports are eliminated and eventually as US and Australian exports to Asia leave Middle Eastern gas looking for buyers... but that's not even close to being a short term solution.

http://online.wsj.com/news/articles/...89130300876450

Another fairly clear assessment:

http://www.forbes.com/sites/kensilve...gainst-russia/

Good summary quote from the BBC link above:

"So, who is more reliant on whom? This has more to do with the exercise of political will rather than of economic leverage."