Brahimi was born in Istog, FR Yugoslavia to Kosovar Albanian parents. He lived in Istok for two years before moving to Zürich, Switzerland along with his mother, brother and two sisters due to the growing tension in Kosovo. Prior to moving, his father had been living for a number of years in Switzerland as a Gastarbeiter. He then signed for local side FC Red Star Zürich in 1997 before being spotted by Grasshopper Zürich in 2007.