Speaking on Atlanta's pregame show ahead of their Wednesday match against Inter Miami CF, Eales said: "I can confirm there's a deal in principle."
Martinez, 27, was not included for the game's roster and is awaiting a medical ahead of his move.
Al-Nassr is one of Saudi Arabia's most prominent teams, having won multiple domestic and continental titles.
Martinez joined the Five Stripes last season from powerhouse River Plate after winning the 2018 South American Player of the Year and helping the Buenos Aires club win the 2018 Copa Libertadores over bitter rivals Boca Juniors.
But his MLS career has floundered, with seven goals and 11 assists across 39 league appearances with Atlanta. He never meshed with manager Frank de Boer, who was let go in July after Atlanta finished the MLS is Back tournament with no points and no goals scored.
Martinez's time in Atlanta did have some high points as he helped guide the club to both the U.S. Open Cup and Campeones Cup in 2019.