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Bauza, who took over as coach of the Albiceleste in 2016, is currently on a tour of European clubs, scouting players as he continues preparations for the 2018 World Cup.
The coach was in Rome this week, and admitted he watched Roma's Coppa Italia victory over Cesena as an opportunity to scout both Perotti and Fazio.
“I watched Roma-Cesena, then went to Lazio and Inter's training grounds," Bauza told Gazzetta dello Sport. "I am going to Turin for Juventus-Inter ... then I am in Madrid, England and France.
“I want to see as many players as possible and if I have the opportunity to speak with their coaches."
Fazio and Perotti have both represented their country in the past, but have not been capped since 2014 and 2011 respectively.
Bauza added: “At Roma I wanted to see Perotti and it’s a shame he got injured.
"Fazio didn’t play against Cesena either, but I know he’s in a very good moment of form and we have been following him for a while.”
Both Giallorossi players have admitted recently that they would like to earn a recall to the national team.
“It's my dream and if I were to get a call-up, it would be reward for everything I've done in my career," Perotti said in an interview in December. "It's hard though because Argentina have some amazing players from the midfield up.
"However, if I keep doing well at a big club like Roma perhaps the coach will take a look at me.”
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