Byram has been injured since the end of the last campaign and is struggling with the problem, but the former Reading boss hopes that it can be managed with injections.
McDermott told the club's official website: "Sam's got a hip problem. He had an injection last week and we'll have a look at it over the next two or three days, but there's a possibility that he'll need an operation.
"We don't know yet, but that could put him out for a period of time. We'll know within the next week and it's a shame for him, but he's only 19 and if he has to be out for a while, we have to do the right thing by Sam."
Leeds tasted victory in their first game of the season when they beat Brighton and Hove Albion 2-1 at Elland Road.