Russia and Georgia are not thrilled with the idea.
Ukraine's pro-Western leaders hope to join NATO but the people of the Ukraine are mixed on the idea. Recent polls show that more than half of the population is opposed to NATO membership.
Today pro and anti-NATO forces clashed during a protest in the Ukraine.
Primary opposition to NATO comes from the citizens of Sevastopol (where the Russian Black Sea Fleet is based) as well as large swathes of Ukraine's Russian-speaking east and south.
The Crimean peninsula where Sevastopol is located was a part of the Russian republic of the Soviet Union until 1954, when Soviet leader Nikita Khrushchev signed it over to the Ukrainian republic as a "token of brotherly love".
That mattered little when both republics were part of the Soviet Union, but when Ukraine gained independence in 1991 it became a ticking time bomb.
Through the 1990s, as the new Ukrainian state established its credentials, Crimea was gripped by periodic outbursts of pro-Russian sentiment but has since been generally calm.
If Ukraine and Georgia are accepted into NATO, Russia will revise is relations with the alliance, Russia's envoy to NATO Dmitry Rogozin said recently. "The NATO eastward expansion at the expense of Ukraine and Georgia is a red line in our relations with NATO, which NATO should not cross. If NATO crosses this red line, relations will not only be spoilt, but they will change drastically."
During the NATO summit in April then President Vladimir Putin hinted that Russia would work to break up Ukraine, should the former Soviet republic join the military alliance.
The follow blurb is from Russia Today.
NATO opponents and supporters clash in Ukraine
Opponents and supporters of Ukraine's entry into NATO have clashed in Crimea's largest city of Simferopol.
Police tried to separate the two parties, which were holding simultaneous meetings in the central square of the city. However, verbal abuse triggered a fight involving about 150 people.
The NATO opponents, mostly communists, threw tomatoes, eggs and cartons of juice at their rivals. They were carrying posters, which read 'NATO Is War Against Slavs' and 'Neo-Fascism Won't Succeed.'