The article states that Trump aims to achieve a ceasefire in Ukraine as quickly as possible, and therefore, officials in Kyiv believe it is "critically important" to secure guarantees that there will be no renewal of Russian aggression in the future.
In particular, this viewpoint was expressed to an American publication by Roman Kostenko, the secretary of the Ukrainian Parliament's Committee on National Security, Defense, and Intelligence, and a colonel in the SBU. According to him, for Ukraine, "nothing is more important" than security guarantees.
He points out that Russia controls about 20% of Ukrainian territory based on the 1991 borders, but Kyiv will not officially abandon its goal of de-occupation. The publication cites earlier statements from Ukrainian President Volodymyr Zelensky, who mentioned that regardless of the path chosen to end the war, "legally, no one will recognize the occupied territories as belonging to other countries."
A high-ranking Ukrainian source for The New York Times (the publication does not disclose their name) stated "more straightforwardly" that while the territorial issue is important for Ukraine, it takes a back seat to the question of security guarantees.
The article also mentions Ukraine's desire to become a member of NATO and notes that there is no objection from the West, but they expect this to happen "not on any accelerated timeline."
Additionally, the article discusses that Russia is unlikely to agree to withdraw from the occupied Ukrainian territories to end the war. It also notes that Moscow has allowed the possibility of starting negotiations, but only after Ukrainian forces withdraw from the Kursk region of the Russian Federation, where military operations have been ongoing since August.