The Black Cats have been busy this summer with 10 new arrivals at the Stadium of Light.
But Di Canio admits he is still searching for a midfield playmaker as well as a left-sided defender to further increase competition at the club.
Di Canio said: "If there is a chance, then one or two more would be welcome and the club is working on this.
"I'm happy up front and at the back and I'm happy in the middle, but we miss something. I hope in the next few days we are going to get something there.
"I'm not worried about having a large squad because I want to have a chance to choose from a group of five rather than only two.
"For me, it's important to have players pushing for their place, and the other players have to maintain their place by doing well daily."
Wes Brown will miss Saturday's opening game against Fulham after suffering a slight recurrence of a knee injury in training last week.
Di Canio, though, was keen to put the player's latest setback into perspective.
"I want to think positive. We couldn't expect to see Wes Brown go all the way through pre-season, but the problem was a knock he received in a session last week, and for that we don't want to risk him.
"Even if he misses the first game, he waited nearly a whole year so it's not an issue. It's important that he's okay and in the next few days he can join the team and be ready to be selected for any match.
"He probably couldn't expect himself to go through all the training, but he never missed a session and he was surprised and happy and so were we.
"It's disappointing obviously, because he did everything until 12 days ago, but it's important there are no problems there."