The report also states the 21-year-old is on the radar of Eredivisie giants Ajax and PSV Eindhoven.
Alvarez has become a staple for his country club America making more than 100 appearances.
The centre-back was able to earn his place in 2018 World cup squad, the youngest one on the list.
He played in all the matches in group stage and his horror moment arrived when he scored an own goal in the defeat against Sweden.
Alvarez has earned 22 international caps thus far. He is highly known for his possession skills and versatility to play either as a centre-back or a full-back.
The Mexican centre-back has made more than 30 appearances this season and scored three goals.
Why Celtic must pursue Alvarez?
Celtic’ defensive option will deplete with the speculated exit of Dedryk Boyata and Filip Benkovic from Park Head.
And Alvarez would team up with Kristoffer Ajer to form a formidable line of defence.
Given that Alvarez is also pursued by Ajax, PSV and Inter, the Hoops may find it slightly difficult to persuade the high-profile defender to Park Head.
Moreover, the Scottish Clubs have never been the preferred destination for the Mexicans in history.
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Neil Lennon, the interim manager of the Hoops, will face his first Old Firm derby in seven years this Sunday.
The Hoops are ten points clear of their arch-rivals Rangers in Premiership table and have set their eyes on the eighth straight league title.