Ramsey has been missing in action ever since he suffered a hamstring injury in the opening-day defeat to Liverpool.
He was initially expected to return following the first international break of the season, but it appears that he has suffered a setback in training.
Coleman, who is set to miss the midfielder for the upcoming World Cup qualifiers, expressed his dissatisfaction with Arsenal's treatment of the player.
"I had an indication that he would only be out for three weeks when he initially did it — that was six weeks ago," Coleman said.
"I have had more information from Sean (Connelly), our head physio who is liaising with Arsenal, that he has broken down in training. We have not yet been given a date on when he will definitely be back.
"I can't be sure he will be back for Serbia (on November 12). I was sure I would have him for this camp. It is frustrating. It is preventable.
"Our physio will get more information. It is hard to comment on whether he was pushed too hard or not enough. I don't know exactly what has happened.
"The disappointment is we expected him to be here."