The Argentine centre forward is also being linked to La Liga giants Atletico Madrid.
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Per TyC Sports, Chelsea are ready to put in a mega offer to tempt City to sell Alavarez.
While he is a favorite of manager Pep Guardiola, he is behind Erling Haaland in the pecking order.
If City do sell, they will have a lack of depth up front, as Haaland is their only other recognized center forward.
As such, they are likely to seek a fee in the region of £80 million for Alvarez this summer.
