The German looked to be in a battle with Liverpool for the highly rated footballer, but they appear to have moved to the front of the queue, with Dortmund playing in the Champions League next season.
Rumours are that Borussia Dortmund have submitted a £12 million proposal, with Ajax holding out for £15 million.
The two sides are, nevertheless, expected to reach an agreement in the coming days, meaning Liverpool are likely to miss out on yet another long-term target.
Borussia Dortmund are forced to rebuild the squad in the summer, with Mario Gotze, Robert Lewandowski and Felipe Santana all set to leave.
Eriksen has had plenty of admirers from top clubs in Europe, after impressing with Ajax and helping them win three Dutch titles in a row.