Foureira has made several attempts to represent Greece in the Eurovision Song Contest. In 2010, she took part in the Greek national final for the Eurovision Song Contest 2010 with Manos Pyrovolakis, performing the song "Kivotos tou Noe". They placed second behind Giorgos Alkaios. In 2013, she performed "Wild Dances" with Ruslana at Eurosong 2013 – a MAD show. She later considered taking part in Eurosong 2015 - NERIT & MAD show, but ultimately did not. She once again attempted to represent Greece in the Eurovision Song Contest 2016 with the song "Come Tiki Tam", but was rejected by Hellenic Broadcasting Corporation (ERT). In 2017, she was rejected by the broadcaster for the Eurovision Song Contest 2017 once again.
Since the beginning of her career, Foureira's ancestral origins have garnered intense speculation from the Greek media. As a member of Mystique, she claimed to be Brazilian. However, she later began claiming that her father was from Athens and her mother from Ioannina, although she had some Mexican ancestry as well. In 2010, reports of Foureira attempting to naturalise as a Greek citizen further increased speculation regarding her origins.