Alfreð joined Breiðablik in 2005, featuring in the club's highly successful youth team alongside future internationals and/or expatriates Gylfi Sigurðsson, Jóhann Berg Guðmundsson, Elfar Freyr Helgason, Guðmundur Kristjánsson, Kristinn Steindórsson, Kristinn Jónsson and Aron Jóhannsson.