The Bafana Bafana star, who is coming off a difficult season with the Urban Warriors, has long been a target of the Brazilians.
However, Ajax chairman Efstathiou has spent the last few days in Europe where he is involved in talks about a overseas move for the player.
“I am specifically in Europe for Rivaldo and we are making progress,” he told ww.soccerladuma.co.za.
No further details have been disclosed.
Coetzee’s contract with the Cape side reportedly expires next month, although his club do have a two-year option to renew the deal.
Meanwhile, Coetzee’s Ajax team-mate Lebohang Mokoena is set to part ways with the club when his one-year deal expires at the end of June.
The 30-year-old winger, who joined on a free transfer last year, failed to establish himself in the team during the course of the season and looks set to leave Ikamva.