Born in Solna with Hungarian roots, Limpar started playing football in Brommapojkarna, famous for its production of footballing talent. He then played for Örgryte, joining in the wake of its sensational Swedish championship title in 1985. Limpar quickly became one of the hottest properties in Swedish football, and as so he was offered the chance to journey to Switzerland with Bern club Young Boys. He followed this up in a one-season spell in Italy with Cremonese during the 1989–90 season.