The 17-year-old has been drawing interest at AIK Solna for his goalscoring prowess.
And the rising star carries some resemblance in his forward play to national hero and Manchester United superstar Ibrahimovic.
Jurgen Klopp's side are one of an array of top European clubs said to be monitoring the striker.
According to Spanish newspaper SPORT, Liverpool face competition from Leicester, Bayern Munich, Barcelona and Real Madrid too.
The Catalan giants have apparently stepped up their pursuit by watching Isak more intently.
But both Liverpool and Leicester are claimed to have continued their own tracking of the player in recent months.