Sunderland have had a bid rejected by AZ for the American international as Paolo Di Canio looks to bolster his attacking options.
Altidore, who has already had a spell in England with Hull City in 2009, enjoyed the best season of his career last term after scoring 23 league goals for AZ.
Italian side Lazio have also been linked with Altidore and, although the 23-year-old is refusing to give anything away about his future, he has hinted he would consider a move to Sunderland.
"It is better for me not to comment on all the rumours, not only with Sunderland, but also with other clubs," said Altidore.
"It would not be a problem for me to stay at Alkmaar because I am having a good time here and I have had two good seasons.
"I have not had any problems with my team-mates and I feel fine here.
"But when you get the possibility to play somewhere else, you always have to think about it.
"In general, you might be happy in your job and you don't think about leaving it.
"But if you have the opportunity to work somewhere else, you will think about it."