McCarthy was stretchered off in the second half of the Blues' draw with West Brom at Goodison Park after bravely challenging Salomon Rondon to stop the striker's shot at goal.
“It is down to the specialist and them saying if and when James can start moving forward," Allardyce told evertonfc.com.
“The specialist will guide us on how far we can go and with a bit of luck we can look forward to James starting the next pre-season with us.
“He has had some time back at home. He will probably rejoin us in the next few days on a regular basis to start getting some mobility into his ankle, particularly because it has been in a set position for such a long time."