The 17-year-old caught the eye of Tottenham scouts after scoring a hat trick against Argentina in the under-17 World Cup in Abu Dhabi.
And the North London club are hopeful they can sign the forward – dubbed the ‘new Zlatan Ibrahimovic’ – for as little as £500,000.
Berisha is regarded as the most exciting young talent in Sweden, scoring an array of stunning goals for both club and country.
As well as his hat trick against Argentina, the young forward also scored an amazing back heel in the semi-final against Hondurus – a goal which drew comparisons with Paris St Germain forward and fellow countryman Ibrahimovic.
The youngster – who reportedly holds both Swedish and Kosovan nationality – has caught the attention of a number of top European clubs since breaking onto the scene.
Tottenham manager Andre Villas-Boas is aware he will face competition for his signature, but remains confident of completing the deal.
The 17-year-old is likely to be one of several forwards targeted by Villas-Boas in January, after watching his team struggle for goals in the opening 11 games of the season.
Sunday saw Tottenham fail to score from open play for the third consecutive Premier League game, as they went down to a 1-0 home defeat to Newcastle United.
The club have also been linked with a move for Brazilian forward Alexandre Pato.