That is what one well-informed source tells me, so I have investigated the matter. The woman involved was one of the most important and powerful of the Soviet era, Yekaterina Furtseva, the first woman to join the ruling Soviet Politburo in 1956, who was also a powerful Minister of Culture who famously banned certain movies and ruined certain actors. On the Politburo she was at least at first a strong supporter of Nikita Khrushchev, providing crucial support for him in some of the battles that went on in the Politburo during the late 1950s, most importantly against an effort in 1957 by Stalinists led by Molotov who wanted to overthrow him. However, in 1960, she turned against him and joined a failed effort to have him removed.
Prior to her elevation to the Politburo, she served as the leader of the Moscow Communist Party, with Khrushchev responsible for putting her into that position after Stalin died in 1953. It was in 1954 that Khrushchev gave Crimea to Ukraine from Russia as a "gift," with the reasons for doing so still a matter of much debate, although ostensibly at the time it was in celebration of the 300th anniversary of the original union between Russia and Ukraine. It has also long been argued that Khrushchev had long dreamed of doing this as a way to please the Ukraine and also to keep the Tatars from returning by offering their land to Ukrainian peasants, and indeed the ethnic Ukrainian population of Crimea did increase after this gift, although they are still only in third place in the autonomous republic behind ethnic Russians and Tatars.
I note that the ethnic composition and history of this in Crimea is far more complicated than most recognize, with Stalin in 1944 removing not only the Tatars who gave it its name, but also Armenians, Bulgarians, and a group that had long predated the Tatars, Greeks, whose presence dated back 2500 years and who called the place "Taurica," or initially "Tauris," after the even earlier Tauri inhabitants, an apparently Indo-European group reputedly descended from the Cimmerians. While Tatars returned starting in the 1980s, the Greeks have only recently begun to return there.
One can make the argument that Khrushchev was motivated in this also because of his personal connections to Ukraine, and undoubtedly this played a role. He was born in a Russian village, but one near the Ukrainian border, and while most sources identify his parents as Russian, some say that he had some Ukrainian ancestry as well. In any case, he was sent by Stalin to run the Ukrainian Communist Party in the late 1930s, and oversaw purges and much else there. It is fully understandable that he may well have become sympathetic to the republic during this period, thus leading to his actions on Crimea in 1954 shortly after he became Premier and before he had fully consolidated his power, still struggling with Malenkov for control, with the latter initially identified as Stalin's successor upon his death.
However, it may well be that Furtseva contributed to this decision. While she was an ethnic Russian born north of Tver who initially joined the Communist Party while working in a Moscow textile mill, she would be sent to Crimea in the early 1940s where she was in charge of an oblast level Communist Party unit there, equivalent to a county in the US. It is likely she first got to know Khrushchev at that time. In any case, he became her patron after the death of Stalin, and she was in Moscow running its party at his behest at the time of the "gift." However, as a Stalin appointee in Crimea in the early 1940s, she may well have supported the deportations of the Tatars, Greeks, et al, and agreed with or even been the source of the idea by Khrushchev to populate the place with more reliable Ukrainian peasants to keep these banished groups who were scattered across Central Asia from returning.
Now, to get to the juicy part. While it is not known for sure to be true, the rumors that the two of them were having an affair at that time were widespread, being reported by the BBC among other sources. While this source is tainted in my view for overdoing conspiracy theories, _The Man Who Knew Too Much_ by Dick Russell provides accounts from other sources reporting this rumor on p. 118, including supposed CIA sources and others beyond the BBC report, the latter a matter of public record. Russell reports on other matters that may or may not be true. One that appears to be true is that she was apparently the main defender in the Politburo of letting Lee Harvey Oswald stay in the Soviet Union when he first arrived there, with this being corroborated by other sources as well. "Oswald's defender" she was called. However, Russell pursues even murkier suggestions that I have not seen reported elsewhere that include claims that she was actually a CIA agent herself and that Khrushchev knew this and used her as a backdoor link for certain negotiations, particularly during the 1962 missile crisis. What undermines the credibility of this last claim is that he had apparently turned against her in 1960, but perhaps she had been rehabilitated, and she was still on the Politburo.
However, in 1954, whether or not they were actually having an affair, Khrushchev was clearly very close to this powerful woman whom he would raise into the Politburo and had already raised to the ruling position in the city of Moscow, who had previously served as a Communist Party oblast chief in Crimea. It is not out of the question that she may have crucially and substantially encouraged and supported this decision of his.
Later Correction: It appears that Furtseva was sent to Crimea in 1949 after he met her for the first time. Thus, her experience there would have been more immediately on her mind in 1953-54 when she was closest to Khrushchev and he was making this decision. She would have been aware of the issue that after the death of Stalin, the deported Tatars and others would want to return to Crimea, and so would certainly have supported a scheme to encourage immigration by "loyal" Ukrainians." In the early 1940s she was married to a military man who left her in 1942 after she bore him a daughter. She was later married to a Soviet diplomat, but later in her life he was reportedly cheating on her and she took to the bottle, dying in 1974 at the age of 63.