Speaking in Uruguay's capital Montevideo, Fernandez said that once he takes office in December, it would be "an honor" to welcome Morales to his country.
Fernandez, who was meeting with Uruguay's President Tabare Vazquez, also extended the offer of asylum to Morales' vice president.
Bolivia has been racked by anti-government protests since Morales won reelection to a fourth term in Oct. 20 elections, and the opposition refused to recognize his victory, claiming fraud.
He resigned as president after his nation's armed forces withdrew their support.
Sensing his life was in danger, Morales requested and received asylum from Mexico, where he landed earlier this week.
"If I had been president (at the time) I would have offered him asylum on the first day," said Fernandez, adding "Argentina is his home."
Fernandez will take office on Dec. 10.