Cabanas, who is also claiming costs for his rehabilitation, suffered a setback earlier this week when a Mexican Football Federation (FMF) tribunal ruled in favour of America over the issue, saying the attack was outside the player's working environment.
"We lost in the first instance, now we're going to appeal," lawyer Gerardo Acosta told reporters.
"We had no hope of winning in Mexico but we have sufficient hopes and arguments to turn this case around at the tribunal for arbitration in sport in Switzerland."
Acosta said America had not arranged medical cover for Cabanas. "It's obligatory and he wasn't covered."
However, FMF spokesman Francisco Rocha said: "For us, the affair is over, the club are freed of any obligation because the other party couldn't prove it was a work accident."
Paraguayan media said the amount of money Cabanas is claiming from America is about $1.3 million.
His wife, Maria Alonso, said recently they barely had enough money to see the family through December and called on Cabanas's former agent Jose Gonzalez to provide documents proving the two men had joint business deals.
Cabanas, 30, had signed a contract with America until 2012, according to Gonzalez.
The player, who had been set to go to the World Cup in South Africa with the Paraguay team in June, was shot in an alleged argument over his form and that of America in the Mexican league.
Cabanas, who survived the attack but still has the bullet lodged in his brain, was moved from a Mexico City hospital after a month to a Buenos Aires clinic. He has since returned home to Paraguay.
