Record says the 26-year-old does not feel that United's project is right for him and would prefer another move if he is to leave Lisbon.
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Al Nassr are among clubs keen.
The Saudi club has followed the striker long-term and wants to make a deal in the summer. However, Al Nassr are not ready to pay his €100m buyout clause.
But Sporting are ready to release Gyökeres for €60-70m.
Arsenal, Chelsea, Liverpool and Manchester City are said to be also interested in Gyökeres.