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Ledley returned from Scotland on Thursday without a contract being signed.
"It's not a done deal yet. Obviously I've got a lot to think about," he said.
"I just came up for a look around but I've been very impressed. Will I be back? We'll see."
The presumption by Celtic that Ledley will be in America wearing their shirt would indicate they are confident he will complete his move.
That will leave City fighting for some form of compensation for the loss of Ledley on a free transfer to another country.
Dave Jones said: "We will try to get compensation through the training rule, battle that out with Celtic.
"You get training compensation when you cross the border and we will be arguing that out. There are set figures with Fifa. We will see where it goes."