Núñez returned to England unexpectedly during the latest international break after becoming involved in reports of tension with the Chile coaching staff.
Córdova has now rejected suggestions that he ordered the 25-year-old to leave, insisting the decision came from the player himself.
“A lot of versions appeared. For a personal matter, he made the decision to leave the squad,” Córdova said.
“I found out the morning after the United States game, and we went to training. He trained and, on the way back, decided to stay so he could go to England, while we travelled here.”
The manager was subsequently asked directly about reports of an argument between himself and Núñez.
“That’s something you have to ask him. You don’t have to ask me,” Córdova replied.
“It was his decision. It’s not that I kicked him out of the national team. It’s not that I had an argument with him.”
Córdova maintained that Núñez is responsible for explaining the reasons behind his departure and said he had no intention of speaking on the midfielder’s behalf.
“I don’t have much more to add because it was a completely personal decision, determined by reasons that he will have to explain,” he said.
“I don’t have to explain other people’s decisions.”
The Chile boss acknowledged that losing a player from the squad was not ideal, particularly during an international window.
“It’s not pleasant when a player leaves. We’re very clear about that,” he said.
Núñez has received support from some Chilean players and local observers during the dispute, while reports have continued to raise questions over what happened behind the scenes.
Córdova’s version nevertheless differs from suggestions that the midfielder was sent home following a confrontation.
The manager said that once Núñez had left, his focus immediately returned to the players who remained with the squad and the preparation for Chile’s final match of the international break against Mexico.
That leaves Núñez as the only principal figure yet to publicly explain his version of events.
For Ipswich Town, the midfielder’s return to England brings the controversy back into the club environment, with questions remaining over whether the disagreement will have any effect on his future involvement with Chile.
Córdova, however, insists the decision to leave was Núñez’s alone.