Well, yes and no. Poland had a medieval institution called the "Gypsy king," in fact an ethnic Polish noble who was placed in charge of surveilling and managing Romani communities. This does not seem to have continued when Poland was partitioned between Russia and the German states, but following the recreation of Poland in 1918, a Polish Romani community leader named Michał Kwiek appointed himself "Gypsy king" and started a dynasty.
This self-appointed leader was taken quite seriously by the Romani of Eastern Europe. In 1937, the heir to the throne Janusz Kwiek was appointed king in an elaborate, formal ceremony in Poland. His cousin explained that "Mussolini, who has promised us Abyssinia, will only take us seriously if we are formally organized and have orderly relations with the Polish state." (Bárány, p.102)
This refers to the fact that when Mussolini invaded Ethiopia, he found a small Jewish community there (the Beta Israel), which made him feel it would be appropriate to deport Italy's Jews to go join them. Apparently the Romani had heard that they would be allowed to settle in Ethopia as well.
While historians report that the "Gypsy king" institution was widely considered legitimate among the Romani, I do not see this statehood project mentioned anywhere outside of the small court of the Gypsy king, nor mention of anyone settling in Ethiopia. Certainly Mussolini was never serious about his Jewish colony idea (much to the disappointment of the Nazis). This contrasts strongly with Zionism, where settlement is generally considered to have begun in 1882. By 1948, Zionism was well-established and had received the formal legal support of Britain and at least diplomatic support from other nations. The Gypsy kings disbanded in the 1960s and a formal meeting of Romani nationalists did not convene until the 1970s, at which point the creation of a monoethnic colony was no longer fashionable.
cited: Zoltán Bárány. The East European Gypsies: Regime Change, Marginality, and Ethnopolitics. See also The Roma Movement in Poland
While the Second World War and the brutal fate of Europe's Jewish population in the 40s were unambiguously central to the formation of the state of Israel, the project of crafting a Jewish nation-state had begun more than a half-century before, a political movement known as Zionism. Consider, for example, a 1881 treatise by early Zionist writer Leon Pinsker titled "Anti-Emancipation," which argued that Jews suffering ethnic violence in Europe should establish a new Jewish state in Palestine.
With the support of sympathetic figures within European nobility, an international delegation met in Switzerland in 1897 &'98 with the specific intention of laying political groundwork. Theodore Hertzl was chosen as leader, and later wrote in his diary: "If I had to sum up the Basel Congress in one word—which I shall not do openly—it would be this: At Basel I founded the Jewish state. If I were to say this today, I would be greeted by universal laughter. In five years, perhaps, and certainly in 50, everyone will see it."(https://www.britannica.com/biography/Theodor-Herzl#ref26685)
Fifty years later, in 1948, the state of Israel was officially founded.
I'm not aware of any parallel movement among European Roma.