Celtic had a £5 million offer for Edson Alvarez knocked back in the January window, according to ESPN.
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The Parkhead side were linked with a move for the 21-year-old earlier this year though it was not known whether a concrete offer was made.
ESPN now claims such a bid occurred but it was thrown out by Club America.
The Liga MX side are said to be holding out for a fee of around £9 million for the 22-cap Mexican international.
Celtic are expected to strengthen their centre-back corps this summer after the departure of Dedryck Boyata and the expiration of Filip Benkovic's loan from Leicester City.