The Shields Gazette reports that Sunderland have offered the teenager a contract, in a bid to head off interest from rivals.
Reports claim that Liverpool, Tottenham, Ajax and Roma are keeping tabs on the highly-rated youngster.
The Halmstad striker scored a hatr-trick for Sweden against Argentina in last month’s under-17 World Cup in Abu Dhabi.
Berisha finished the tournament as top scorer with seven goals.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?