The right-back picked up a thigh problem in the win over West Brom three weeks ago but he has been undergoing intense rehabilitation and now looks to be on course to return soon.
Everton's head of physio Mick Rathbone is confident Hibbert will return to training towards the end of next week.
"Tony's doing well," said Rathbone. "It was quite a bad thigh strain. He's 23 days into it and we talked about four to six weeks, so he's making good progress.
"Hopefully he will train towards the middle of next week."
Hibbert's return would be a boost for boss David Moyes who faces an anxious wait for the return of his international players.