A scan on Jones' injured hip late last week revealed a tear in his cartilage. An operation had looked a possibility at one stage but McCall says that City are confident the issue can be resolved with an injection in the area.
Should everything go to plan, McCall believes that Jones should be back out on the training pitch in around two weeks.
McCall said: "We've sought out the opinion of a couple of specialists to try and find out the best course of action.
"The last thing you want to do is operate. He has also been feeling better in the last few days.
"The most likely option for Alex is to have an anti-inflammatory injection in the area of discomfort. We hope that will help speed up the recovery process.
"He will rest after that and then look to do a bit of CV (cardiovascular) work.
"The aim will be for him to join in with training in the next ten days to two weeks.
"Alex is comfortable with that plan - he is desperate to get back involved."
While Jones looks set to miss out again at the weekend, defender Nathaniel Knight-Percival could be included in City's travelling party to Bristol Rovers after returning to training this Thursday.
Knight-Percival is back in contention after missing the last three games with an ankle problem.
McCall added: "He did all his CV and functional work with (Chris) Shorty on Monday and Tuesday, and then joined in with us today (Thursday).
"He probably could have joined in earlier but he came through with no problems this morning.
"He is back and hungry to get in the squad again."