The 30-year-old admitted he was looking for a Goodison Park exit after falling out of favour under Roberto Martinez, prompting the Hammers to make a move while they are short on defensive cover.
Heitinga's only two appearances for the Toffees this season have come in the Capital One Cup, but he rejected a proposed switch to Upton Park and will wait for other offers with six months remaining on his current deal.
"At my age it's important to make the right decisions," he said in a statement released via his agents, Sport Promotion.
"Then it's not all about the money, as that wasn't a problem at West Ham United. You have to be fully convinced that you will make the right step and I didn't have that.
"Therefore I have cancelled (the move to) West Ham United and we will now wait for the interest of other clubs.
"The interest is there already, so I am confident I will find another club before January 31st. That's the date the transfer window will close."
Heitinga also admitted that he still has hopes of representing Holland at the summer's World Cup and that will play a factor in deciding his next club.
"I want to play every game again, as I am still hungry for the ball," he said.
"I am fully fit and a player on top of my strengths. I want to go to the World Cup in Brazil.
"I know that national coach Louis Van Gaal requires his selected players playing weekly.
"At the moment, that's not the situation at Everton and therefore I am now looking for other options to get a successful continuation of my career."