America has received an offer and a verbal agreement is in place between the two clubs and the player to take the 21-year-old to the Eredivisie, according to the sources.
Alvarez has been regularly linked with Ajax this summer and Dutch newspaper De Telegraaf confirmed personal terms had been agreed to early Monday, with the outlet reporting that the offer from Ajax is almost $17 million and the contract will be for five years.
Sporting director Marc Overmars was quoted in Eindhovens Dagblad saying that the club is interested in Alvarez and that a deal is possible, although he denied that the Mexican would be a direct replacement for Matthijs de Ligt, who is expected to join Juventus.
"Edson Alvarez is a player we like," Overmars said. "I think he's at a good age, 21, is a regular international for Mexico and we've known about him for a while because we've been following him."
Alvarez rose up through the Club America youth academy, scoring twice in the 2018 Apertura final against Cruz Azul to help win the title for Las Aguilas. The Estado de Mexico native made his Mexico debut in 2017. He then featured for El Tri at Russia 2018 and was a regular in the team that won the Gold Cup this summer.
Alvarez had previously been linked with Wolverhampton Wanderers and West Ham United.