Kaviedes should replace veteran midfielder Alex Aguinaga, who is nursing a muscle injury.
I am in good shape and I know the Mexican team well - it's a match I'm looking forward to
The 25-year-old striker, who plays professionally for Mexico club side Puebla, helped to lead Ecuador to its World Cup finals debut.
However, coach Hernan Dario Gomez's defensive tactics for the team's opening match, a 2-0 defeat by Italy, cost him a place in the team.
"I am in good shape and I know the Mexican team well," Kaviedes said on Thursday. "It's a match I'm looking forward to."
Team officials grew nervous after striker Carlos Tenorio left the training session complaining of a left arm injury. It was unclear how he was hurt.
The Ecuador team doctor Patricio Maldonado said that X-rays showed it was not serious enough to keep him out of Sunday's game.
Meanwhile midfielder Alex Aguinaga will almost certainly miss the match on Sunday as he nurses a right thigh injury.
Maldonado said he would not permit Aguinaga to play until he had completely recovered from his injury.
"If he plays and the injury gets worse, he will be out of action for two or three months. I won't permit taking that kind of risk," he said.
"I'll do the final examination on Saturday and we will know if Alex can play on Sunday.
"Sadly, we are running out of time ... and Alex still isn't well."
Meanwhile Mexico reported no injury problems and expect to be at full strength.
Coach Javier Aguirre said the only slight doubt was over striker Jared Borgetti who came off during the Mexicans' opening 1-0 victory over Croatia.
"It was just a slight knock, but I am okay and it is nothing serious," said Borgetti.
"I am ready to play if I am selected against Ecuador."
Aguirre is considering recalling Johan Rodriguez to his side after the midfielder missed the Croatia game through suspension.
Forward Jesus Arellano was also suspended for the Croatia clash and will serve the second match of his two-game ban on Sunday.