From The horse, the wheel, and language by David W. Anthony (2007), p. 385:
Linguists have identified loans that were adopted into the early Finno-Ugric (F-U) languages from Pre-Indo-Iranian and Proto-Indo-Iranian (Proto-I-I). Archaeological evidence for Volosovo-Abashevo contacts around the southern Urals probably were the medium through which these loans occurred. Early Proto-Indo-Iranian words that were borrowed into common Finno-Ugric included Proto-I-I *asura- ‘lord, god’ > F-U *asera; Proto-I-I *medʱu- ‘honey’ > F-U *mete; Proto-I-I *čekro- ‘wheel’ > F-U *kekrä and Proto-I-I *arya- ‘Aryan’ > F-U *orya. Proto-Indo-Iranian *arya-, the self designation “Aryan,” was borrowed into Pre-Saami as *orja-, the root of *oarji, meaning “southwest,” and of ārjel, meaning “southerner,” confirming that the Proto-Aryan world lay south of the early Uralic region. The same borrowed *arya- root developed into words with the meaning “slave” in the Finnish and Permic branches (Finnish, Komi, and Udmurt), a hint of ancient hostility between the speakers of Proto-Indo-Iranian and Finno-Ugric.
Here Anthony is referencing Koivulehto (2001) and Carpelan and Parpola (2001).
Works Cited:
Anthony, D. W. (2007). The horse, the wheel, and language: how Bronze-Age riders from the Eurasian steppes shaped the modern world. Princeton, New Jersey: Princeton University Press.
Koivulehto, J. (2001). The earliest contacts between Indo-European and Uralic speakers in the light of lexical loans. In C. Carpelan, A. Parpola & P. Koskikallio (Eds.) Early Contacts between Uralic and Indo-European: Linguistic and Archaeological Considerations (pp. 235-263). Helsinki: Suomais-Ugrilainen Seura.
Carpelan, C., & Parpola, A. (2001). Emergence, contacts and dispersal of Proto-Indo-European, Proto-Uralic and Proto-Aryan in archaeological perspective. In C. Carpelan, A. Parpola & P. Koskikallio (Eds.) Early contacts between Uralic and Indo-European: Linguistic and archaeological considerations (pp. 55-150). Helsinki: Suomalais-Ugrilainen Seura.
[...] also this earlier post on historical use of *arya as an Indo-Iranian [...]