Magallan, 26, joined Ajax from Boca Juniors in January 2019 for €9m plus bonuses, theoretically as a replacement for Matthijs de Ligt.
But the Argentine centre-back disappointed in Amsterdam and has appeared just six times in one and a half years.
He was loaned to Alaves in Spain for the entire 2019-20 season, making 17 league appearances.
According to Gianluca Di Marzio, Crotone are signing Magallan on loan and have an option to buy for €9m.
Magallan will arrive in Rome over the next few days for his medical tests.
He will be the first major signing for Crotone, who won automatic promotion to Serie A last season.