He has already been ruled out of Saturday's match against the Pacific Islanders, but is targeting a return for the Canada game on Friday week - eight days before the All Blacks.
"I'm pretty optimistic really," claimed Jones.
"If it keeps on improving like this I'm going to try to target the Canada game, but I'm not sure whether that is realistic at this stage. I've never had an injury like this before.
"This has been classed as grade one damage, whereas grade three you would require a knee reconstruction.
"I'm really happy really because on Sunday morning it was stiff and I was struggling to walk. But the last couple of days it has come on leaps and bounds.
"Having access to a physio in the camp makes a big difference."
Jones said he was devastated to limp off so early in his first game as official Wales captain.
"I was gutted on Saturday because I did so early in the game. I made a tackle and thought: 'something isn't right here'.
"I could run okay in straight lines, so I knew it wasn't really serious, but I couldn't move from side to side.
"I gave it five or 10 minutes but I just wasn't able to run it off."
Jones admitted he was hugely impressed by the performance and attitude of his understudy James Hook, who kicked 13 points on his home debut.
"To be fair he had an awesome game and his composure was superb. If you look at every kick he had, he didn't have one in front of the posts to ease his nerves.
"Not only did he kick brilliantly, his distribution was superb and he kicked at the right times, so the balance and the mix in his game was good.
"We played the first 20 minutes like a team who had not been together for a while, but what was great was the way we came back and had a belief in our game.
"He is a great professional. He has got a great work ethic and has an appetite to learn.
"He is a very level-headed individual and a great guy."