The striker left Chelsea at the end of last season and looks set to move to the Amsterdam Arena if the two parties can agree personal terms
The striker has been a free agent since leaving Chelsea at the end of last season, but the Amsterdam club's sporting director Marc Overmars revealed they had spoken to the player on Saturday.
De Boer has now given his vocal backing to the pursuit of the Cameroonian star, with the former Inter and Barcelona man set to watch the club's clash with Vitesse Arnhem on Sunday.
"It would be great for us if we could get a player like him," De Boer told Fox Sports.
"He has still got the ambition to show what he's got. He must take a role as leader, show our young players what it means to be a professional football player.
"He must be an example for our youth. I want him to show why he wants to come to us. We're looking for a striker and if it will be him, that would be great."
Eto'o has also been offered to Ajax's Eredivisie rivals PSV, though they appear to be in pole position for his signature after the Eindhoven club baulked at his €2 million a year salary demands.
PSV's technical manager Marc Brands added: "I don't know who represents him but yesterday we had an offer from his people.
"We are already full in that area with Jurgen Locadia and Luuk de Jong. €2m net plus add ons was the salary demanded and that was too much for our club - it's more than double our salary cap."