El Tri will take on the Albiceleste in Cordoba on Friday, before the two sides play again on Tuesday in Mendoza.
Though Argentina will bring plenty of attacking talent to the pair of home friendlies, the Barcelona star will not be with the side once again, continuing his post-World Cup hiatus.
"It would've been really nice to face Messi," Alvarez said in a press conference Wednesday. "But his health comes first. Personally, it would've great to play against him."
Alvarez may get the chance in the future though, with Argentina general manager Jorge Burruchaga telling Goal on Wednesday that the 31-year-old will return to the national team in 2019.
"It's impossible that he will not be in the national team again," Burruchaga said of Messi.
"I'm sure that next year, he will be in the Argentine national team again."
Along with Messi, Sergio Aguero and Gonzalo Higuain will also miss out on the two friendlies, but Argentina still have Lautaro Martinez, Paulo Dybala and Mauro Icardi as options in attack, along with others.
Alvarez is looking forward to the challenge of facing a quality opponent away from North America, with the majority of El Tri's friendlies played in the United States or Mexico.
"We've shown that in adversity, when we are the underdogs we step up," the 21-year-old said.
"I like these challenges... what better way to show our quality than now, against a great team in front of their fans? We all want to play the game already."