Turkish side Fenerbahce almost landed the 29-year-old defender last summer.
Heitinga, who has a year left on his Goodison deal, said: "I've had my worst season since I joined. I don't want to extend my contract because it would mean they'd be my final club outside Holland.
"I have played in Spain and England, so maybe it's time for somewhere else. If Fenerbahce come in again, they're an option.
"I was close to joining them last summer.
"Everton seemed ready to let me go - but then the chairman told me 'you're staying'.
"I had been voted player of the season but David Moyes left me on the bench."