The 20-year-old midfielder spent time on trial at the Premier League club during the close-season.
However, Victor Marulanda has confirmed that Perez has been refused a work permit and will therefore not be moving to the Emirates Stadium.
When asked about the Colombia Under-20 international, Marulanda told winsports.co: "We already knew that and were waiting for the response, but that wasn't possible and the player will keep working with us.
"The possibility of joining Arsenal has been ruled out."
Nevertheless, Perez could still be on his way from the Estadio Atanasio Girardot Medellin, with Marulanda confirming he is of interest to two other sides.
"There are two clubs interested in him, it's true," he said.
"If there is any other concrete possibility, he will leave."
Perez featured in Arsenal's 3-1 friendly win over Manchester City on Saturday.
