The Italian revealed he turned down an offer for the midfielder in the summer, and wants him to show the ability to "play good football" before he picks him again
After struggling with a knee injury which kept him out for much of the latter half of last season, it had looked as though Cattermole would be leaving the Stadium of Light.
While there was an offer on the table for the 25-year-old, Di Canio believes there is room for him in his plans, providing he subscribes to the Italian's leadership.
"We have to be honest, he wasn't in the plan but last week I spoke with him for half an hour, man to man," Di Canio explained.
"I told him to have a future here he had to convince me because my regime is completely different to what he had until last year.
"I said now you can be a part of a squad that wants to play good football. You can be better than before. It's up to you.
"You have to jump. You have to back my regime. I decide the discipline, the behaviour, the rules. But we will be stronger than before."
Di Canio, whose side are bottom of the Premier League and without a win, came close to allowing the midfielder to leave.
However, Di Canio's desire for an English presence within his side persuaded him to reject the offer and he has urged Cattermole to demonstrate a number of qualities before he returns to Sunderland starting XI.
"I said no [to the offer], I have to be honest 10 days ago the answer would have been yes, but I need British players," he continued.
"I need the quality, the intensity. I need the fire. I've said to Lee Cattermole show me this character, this quality, this professionalism, this desire, and you will start games.
"Potentially Lee Cattermole's a better player than he maybe even thinks he is. In the last training session I see he can pass the ball. But it's important he works very hard. He has to listen."