"He is improving today, which is good news," said Celtic boss Martin O'Neill.
"We'll take it a day at a time and if he can't make the run of fixtures that we have then we can't do anything about that.
"If he continues to make the same sort of recovery that he is at the minute then I'll be delighted.
"It is better than we hoped, but as of yet we have no idea how long he will be out for."