The answer might depend on how you define Europe, what period you define as pre-Roman, and what evidence you require to accept the existence of a kingdom at a given place and time. I'll assume empire here refers to a territorially large state with a powerful autocratic ruler. I'll assume pre-Roman means antedating 750 BCE, the traditional founding date of the kingdom of Rome by Romulus.
Armenia isn't always classified as being part of Europe, but the kingdom of Urartu, a rival of the Neo-Assyrian empire, existed there from the 9th to 6th centuries BCE. Its capital (from the time of Sarduri I) of Tushpa was very close to the modern-day city of Van. The Kingdom of Colchis in western Georgia may be attested in Urartian records as Qulḫa, indicating it was established before the mid 8th century. Away from the Caucasus, the Amarna correspondence includes letters to and from a king of Alašiya in modern-day Cyprus. This kingdom was a major source of copper and the island was an important part of trade routes in the Bronze Age Mediterranean.
It's difficult to identify kingdoms where we don't have written sources that can describe the political organisation in a region, and we can't presume that the later existence of a kingdom or the tradition of a kingdom being there is demonstrative without carefully assessing the evidence. In Athenian mythohistory, with a chronology determined by Hellenistic authors, Cecrops I was the first king and ruled Athens in the 16th century BCE. He also had a serpent's tail. Two column bases found in the foundations of the Archaic Temple of Athena on the Acropolis suggest there may have been a bronze age 'palace' there, but there's no certainty regarding what kind of building it was and what it was used for.
Similar issues trouble the early history of Macedon. Herodotos claims the first king was Perdikkas I (supposedly early 7th century BCE). According to Polyaenus it was Argaeus I (in Herodotos, Perdikka's successor), and according to Pausanias and many later authors it was Caranus, who might have ruled in the 9th and early 8th century BCE. Caranus was also the route by which the Argeads claimed descent from Heracles. However, the first Macedonian king who we can firmly state truly existed and ruled as a notable king is Amyntas I, who issued coinage, submitted to Darius I, and engaged in diplomacy with the Athenians. However, his reign was in the late 6th century BCE, long after the 750 BCE cutoff date I am using. Should we use his dates for the purpose of this question, or accept the traditions of the rulers before him? There's no evidence to suggest he was responsible for consolidating the kingdom, but we don't have any evidence outside much later Macedonian traditions for the period before him.
One probable candidate is the Ahhiyawa kingdom mentioned in letters of the Hittite Empire dating to around the 13th century BCE. We think this polity was located in Mycenaean Greece, and the Hittites were willing to use terminology implying that the king there was much more than a petty chieftain. But we don't know who this 'Great King' was, how they ruled, or what they ruled over. Our best guess is that the figure of the wanax in Linear B texts referred to someone we could reasonably call a king, and that Greece at the time consisted of a number of such figures. In the epilogue to the 2019 book From 'LUGAL-GAL' to 'wanax': Kingship and Political Organisation in the Late Bronze Age Aegean, Drs. Jorrit Kelder and Willemijn Waal suggest that the most likely system of political organisation was of a unified Great Kingdom with hegemony over the region, based out of Mycenae or Thebes (or possibly Mycenae having an earlier Hegemony and Thebes a later one). However, they acknowledge that this is currently conjectural given the lack of decisive evidence in the texts.
When it comes to the Minoans, the coming of the Mycenaeans brought the wanax-system to Crete, but we can't project this backwards in time and we're very much in the dark about their system of governance before the 15th century BCE.
How about western Europe? As far as I know the earliest king there who we have good reason to suppose existed was Arganthonios (7th-6th centuries BCE?), king of Tartessos, who is mentioned by Herodotos as having welcomed the Greeks to Iberia, where the Phoenicians were already established. This was more than a century before Herodotos started writing, however, and whether he really was a king or some other form of representative might have been lost in translation and transmission.
Undoubtedly many kingdoms have been lost to time, and some states whose governments are uncertain were likely to have been kingdoms. I've tried to make some suggestions that might fit your criteria depending on the three factors I mentioned at the start of my answer. I hope at least some of this has been useful to you, even though I haven't been able to give you anything decisive!