The teenager striker has already stated that he has offers from Liverpool, Sunderland, Tottenham and Celtic - but he now says trial offers from Arsenal and United have been spurned, whilst he is also considering an offer from Real Madrid.
Halmstads younster Berisha was recently top-scorer at the Under-17 World Cup, but he has indicated he wants to play in the first-team at whichever clubs he joins.
"It feels like the big clubs are moving," Berisha told Sportbladet.
"Inter Milan, Juventus, Real Madrid, Sevilla and Villarreal have indicated that they are interested.
"It is terrific. Real Madrid is my favourite since I was a child, they are the favourite club for the entire family but it is only an interest and I don't know if they want me to come on a trial.
"Juventus and Sevilla are more serious, they have given me offers, but the money is not the most important."
Despite the offers from around Europe, Berisha seems set on England.
"The most important is the football education, I believe England would be the best option," he said.
"But I have rejected other clubs who have invited me for trials. For example, Arsenal and Manchester United. It is Real Madrid now, the club of my dreams.
"I am keen to go there, but I think I will turn it down, unfortunately. I do not know, maybe I will go there anyway."