The Western Ukrainian region Transcarpathia can one-sidedly decide to be part of the European Union based on a future rerun of the 1991 Transcarpathian general regional referendum which would mean that Ukraine would lose the territory.
Fueling internal tensions within Ukrainian society is a recurring element of pro-Kremlin disinformation. The disinformation case above is aimed at undermining Ukraine's national identity by arguing that the country is losing territories both in the East and the West.
Transcarpathia, which is Ukraine's westernmost region, is heavily populated by ethnic Hungarians and has not made and cannot make any official or semi-official moves to apply for EU membership on its own.
According to its Constitution, Ukraine is a unitary state. This means regions do not have authority to decide on these matters. This was reinforced by the Ukrainian Constitutional Court of Ukraine on March 14 2014, when they declared the 2014 Crimea referendum contradicted the Constitution. The court declared unconstitutional the Resolution of the Verkhovna Rada of the Autonomous Republic of Crimea No. 1702-6/14 “On holding of the all-Crimean referendum” dated March 6, 2014.
The Judgement of the court says the following: "Any changes to the territory of Ukraine shall be resolved exclusively by the all-Ukrainian referendum (Article 73 of the Constitution of Ukraine). Authority to call the all-Ukrainian referendum on issues indicated in said Article of the Constitution of Ukraine belongs to the Verkhovna Rada of Ukraine (paragraph 2 of part 1 of Article 85 of the Fundamental Law of Ukraine)".
No territory or country or region within a country can decide to voluntarily join the European Union. According to the EU membership process, formal applications can only be submitted by the incumbent government of the applicant country.
See previous cases about Transcarpathia here.