The Denmark international had been heavily linked with a move Borussia Dortmund before Jürgen Klopp signed Henrikh Mkhitaryan as a replacement for Mario Götze.
Liverpool have been regularly linked with the 21-year-old this season after the midfielder scored 13 goals and made 18 assists in Ajax’s title-winning season.
With Brendan Rodgers missing out on Dortmund’s new Armenia international, the Reds are believed to be stepping up their pursuit of Eriksen, and De Boer hinted the final decision over a move rests with playmaker.
“It is up to Christian what he wants,” said De Boer. “If he feels good going to Liverpool, then it is up to him.
“I would want nothing more than having him with us for a few more years.
“But we realise the interest in this kind of player is huge. And I can also understand that he wants to make another step in his career. I can’t stop him.”
Eriksen, who has been heavily linked with a move to Liverpool in recent months, has scored 29 top-flight goals over the past three seasons to help Ajax win three successive Eredivisie titles.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news