The England Under-21 international has been out for seven weeks after suffering the injury during the closing stages of a Champions League game against Standard Liege, and had been expected to need around three months' recovery.
"I feel fine at the minute, and have been doing some work in the gym," Gibbs told Arsenal TV Online. "Hopefully if the results come back okay, I can get on and really start getting [match] fit again."
Gibbs revealed he had struggled with being out of action.
He added: "I did not deal with it that well, because this is my first time I have been out for a long time. But your friends and family are there, and they help you get through it.
"I have been into the training ground recently, and seen a lot of the players. It is good when you are around the team.
"To come back into the changing room, to get involved again makes you feel back at home."