According to AS, Arsenal have already spoken to the Swedish striker’s representatives, but Los Blancos have now joined the race for his signature.
With their debts mounting, Real are reluctant to spend too extravagantly this summer and have identified Isak as a more affordable alternative to Borussia Dortmund’s Erling Haaland or Paris Saint-Germain’s Kylian Mbappe.
The 21-year-old is known to have a £60million release clause in his contract and Arsenal are one of several clubs who are considering activating it.
Mikel Arteta is keen to rejuvenate his squad after a disappointing season ended with the Gunners down in eighth, missing out on a place in European competition.
By his own high standards, Pierre-Emerick Aubameyang had an indifferent campaign, and Alexandre Lacazette, who has one year left on his contract, could be leaving the Emirates.
If Lacazette does depart, Isak would certainly bring some youthful energy to Arsenal’s forward line and excite the club's supporters.
The former Dortmund man has been one of the breakout stars of the Euros, catching the eye with his skill, close control and physical presence.
Although Isak is yet to score at the tournament, he has been the focal point of Sweden’s attacks as they surprisingly topped their group ahead of Spain.
His performances have built on an exceptional season at Sociedad, where he scored 17 goals in 34 appearances as they finished fifth to qualify for the Europa League.
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