Radio Marca reports the Spaniard is set to leave City in the summer transfer window.
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Manchester City sporting director Hugo Viana is ready to listen to offers for González.
City are seeking to raise €60m from his sale, with Gonzalez arriving in January 2025 from Porto.
This season, González has scored one goal in 21 league appearances, 15 of which have come from the start.
His contract currently runs to 2029.