Ramsey pulled out of their friendly win over Austria with an ankle problem.
But Coleman does not believe the injury is too serious, although he is unsure if Ramsey will be fit for the Gunners' clash with Sunderland on Saturday.
"I don't know if he will be ready for the weekend, it's a tough one but maybe if his calf settles down," said Coleman.
"We maybe could have played him tonight but if something happens and we send him back injured it is not ideal. We are trying to build relationships with clubs.
"When the doctor looked at it and red-flagged it, we could not take that risk. He may have a chance for the weekend but I don't know."