The young Dane is a top target for City chiefs.
Eriksen said: "I think many other players would have said 'Yes' to City's offer, but I had my own reasons for turning them down.
"I remember my agent calling me to tell me that they had come in for me, but I told him straight away that I did not see any point in moving to Manchester City - and I still don't. At the end of my career, we will see if I took the right decision.
"But I feel much more at home at a club like Ajax. I really don't want to swap this club for another yet."