Altidore scored 23 goals last season, generating interest from a number of clubs in England, Germany and Italy, including Lazio.
That interest increased when the 23-year-old scored what proved to be the winner in the KNVB Cup final against PSV Eindhoven, in which AZ triumphed 2-1.
However, Sunderland appear to have stolen a march, with a source close to the Black Cats indicating that they are in advanced discussions with the former Villarreal striker.
That follows confirmation from Altidore that he would entertain a return to the Premier League following a loan spell with Hull City in 2009-10 that saw him score just once in 28 games.
He has suffered racist abuse in Holland and he would welcome a return to England.
Jozy Altidore: "It is a fantastic league - anyone will tell you that.
"If you look at everything, the Premier League is probably the biggest league in the world. Everybody knows that, and it would be a pleasure to play in a league like that again.
"I think I was 19 or just turned 20 [when he last played in the Premier League] and I had not played in Europe before that. I have come a long way since then.
"I am almost a different player, and I have learned a lot. So I don't think there is any resemblance to that time if I went back to the league any time soon."