Bardghji, 19, hasn't been seen this season after he suffered a knee injury in May last year. However, he has now returned to training at FCK this past week.
Mundo Deportivo says as many as 13 clubs across major European leagues are showing interest in the Swede.
Spanish giants Atlético Madrid and Barcelona have Bardghji on their radar. The former is said to have made a signing attempt in January.
In the Premier League, there is Manchester City, Manchester United, Chelsea, Aston Villa, Brighton and Newcastle United.
In the Bundesliga, it's the giants Bayern Munich and the reigning champions Bayer Leverkusen .
France's Olympique Marseille and Italian clubs Atalanta and Juventus are also eyeing the 19-year-old.
Currently, Chelsea is in the best position in the hunt for the Swede, according to Mundo Deportivo.