The 21-year-old enjoyed a strong 2020-21 campaign at club level, finding the back of the net on 17 occasions in 34 La Liga appearances.
Isak has also made a positive impression in Sweden's opening two matches at Euro 2020, and both Liverpool and Arsenal have recently been credited with an interest in his services.
According to AS, Chelsea are also keen on the forward, who has a release clause of €70m (£60m) inserted into his current deal with Real Sociedad.
Isak found it difficult to make his mark at Dortmund after a switch from AIK in 2017, but he impressed during a loan spell at Willem II before joining Real Sociedad on a permanent deal. body check tags ::