The Halmstads striker, who is yet to make his senior debut, is rated as one of the top young players in Europe having finished as top-scorer in last year's Under-17 World Cup.
Arsenal, Manchester United, Liverpool, Tottenham and Sunderland are the English clubs who have shown an interest in recent weeks - whilst Celtic, Inter Milan, Juventus, Real Madrid, Sevilla and Villarreal were also reportedly keen.
However, Berisha says his options are now down to just two clubs.
"One club is from England and one is from Italy." Berisha told Fotbollskanalen.se.
"I am negotiating with both right now, but I have not decided which of them it will be.
"I will probably do that in a week's time. I am really keen to play now and want it to be sealed soon."