The England international is running down his Palace deal this season and being courted by Europe's biggest clubs.
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Bayern Munich, Barcelona and PSG have all been mentioned as potential Bosman destinations, along with Liverpool, which had a deadline day deal for Guehi blocked by Palace after a £35m offer was initially accepted.
The Times says City are now making their interest known to Guehi's management team.
City chiefs accept they need to find a new centre-half, given John Stones' fitness concerns and see Guehi as a potential replacement.
Indeed, it's suggested City sports director Hugo Viana views Guehi as their top defensive target for 2026.