The influential midfielder has started every Championship game this season following his arrival from Preston but was forced off after just seven minutes of Saturday's 1-0 home win over Swansea.
Mckenna has suspected knee ligament damage and Davies is waiting to learn how long he will be without the 32-year-old.
"It is not good for McKenna, it looks as if it is ligament damage. We could be looking at a serious amount of time. It could possibly be season-ending," said Davies.
"He has been a wonderful captain for us but that is why you need a squad. We talk about the need to bring in faces at certain times because we know these things will happen.
"We need to bring in a replacement. Not only do we need to bring in a replacement for McKenna but I still believe there are other gaps in the squad. We will have to sit down and identify players we might be able to get and put it to the transfer acquisitions committee."
Source: Team Talk
Source: Team Talk