De Boer, 45, has had the final year of his contract cancelled with the Amsterdam outfit after they dramatically lost the Eredivisie title on Sunday.
Victory over De Graafschap would have sealed a fifth title in six years for De Boer, but they only drew and PSV Eindhoven swooped in to take the crown.
De Boer's agent recently claimed that he would "love" to take over at Everton, and the former Barcelona defender said that he would "see what comes [his] way".
"I began to realise it was time for something else," De Boer told Ajax's website. "That is better for me and I think also for Ajax.
"What I will do, I do not know yet. A year without a club is also an option. I'll see what comes my way."
Everton are thought to be considering the future of Roberto Martinez, having won just one of their last 10 matches.