The Swedish forward, 21, is enjoying a breakthrough season in La Liga, with 12 goals in the Spanish top flight this term.
That includes 10 in his last nine games — a run which has prompted big interest from across the continent.
Sociedad paid Borussia Dortmund £6million to take Isak in 2019 but he is now rated at around 10 times that figure.
Dortmund are understood to have an agreement in place to resign the player at the end of each season for around £25m but Isak has said he does not want to return to the Bundesliga club.
City are keeping tabs on his progress and, if they decide to make a move this summer, they are likely to offer cash and a player, says the Mirror.