The Argentinian outfit are among 12 sides contesting a preliminary round to reach the group stages of South America's biggest club tournament.
The likes of Boca Juniors, Guadalajara and reigning champions Santos lie in wait for the successful qualifiers when the group action gets under way on February 7.
The first match of the qualifying round pits Arsenal in a home tie against Peruvian outfit Sport Huancayo, and Campestrini is desperate for a comfortable win in front of their own fans.
"We are preparing for the first home game and I hope we can score a number of goals," he told celesteyrojo.com.ar.
"We know this is a difficult season for us. We are playing for important goals and we cannot put the domestic league aside.
"But it is important for us because we want to make it into the group stage and qualify from it, something Arsenal have never achieved before."
Should Arsenal prevail over two legs, their reward would be a berth in Group Four alongside Boca Juniors, Fluminense and Zamora.
Also on Tuesday, Paraguayan side Libertad travels to Ecuador to meet El Nacional with the winners set to join Nacional, Vasco da Gama and Alianza Lima in Group Five.
On Wednesday, Internacional and Colombia's Once Caldas meet in Brazil.
Inter won the title in 2006 and 2010 and Once Caldas lifted the trophy in 2004, and Inter coach Dorival Junior told Finalsports.com.br: "The Copa Libertadores is the thing all coaches want to achieve.
"I helped other teams to qualify but never worked on them during the championship.
"The best teams in America play this tournament. This is a big challenge."
Once Caldas boss Pompilio Paez says the team have what it takes to qualify.
He told oncecaldas.com.co: "We have plenty of motivation. We've prepared very well for this match.
"It is not easy to start a tournament. The teams are not fully fit, but we think we have the right team and we'll compete in the best way to represent the club and Colombian football very well."
Inter and Once Caldas are vying for a berth in Group One alongside Santos, Juan Aurich and The Strongest.
Elsewhere on Wednesday, Chilean side Union Espanola host Mexico's Tigres for a berth in Group Three, which also contains Universidad Catolica, Junior and Bolivar.
Brazilian's Flamengo face a difficult visit to Real Potosi of Bolivia, where a place in Group Two with Emelec, Olimpia and Lanus is at stake.
On Thursday, five-time champions and last year's runners-up Penarol meet Venezuela's Caracas in Uruguay with a place in Group Eight alongside Universidad de Chile, Godoy Cruz and Atletico Nacional the prize.