The 32-year old has had a number of injuries in recent years during his spells at Newcastle and West Ham, and he was stretchered off five minutes into his Loftus Road debut against Bolton on Saturday but Cox says he is showing positive signs.
Cox told reporters: “At the time, Kieron said he felt a popping sensation, so he understandably feared he had broken a bone in his foot.
“But the early indication we are getting is that the injury certainly isn't as serious as first feared.
“You can have that feeling with ligament damage as well. At first we thought it was a fracture but we had an X-ray on the day and an MRI.
“That's shown there is no bone fracture but the foot is a very dextrous part of the body and there are a tremendous amount of ligaments involved.
"We are cautiously optimistic at this stage. If it does prove to be what we believe it is, we are looking at him returning to training in days rather than weeks."
Dyer broke his leg in two places during an FA Cup tie against Bristol Rovers playing for West Ham in 2008 and he has spoken of his determination to overcome his injury problems.