The 45-year-old made controversial remarks about the club and its players in a television interview last week.
Di Canio was dismissed from his post at the Stadium of Light in September after just six months in the job, having won just three of his 13 games in charge.
His replacement, Gus Poyet, has guided the team to the final of the Capital One Cup after beating Manchester United on penalties last Wednesday.
A statement from the club read: "Sunderland AFC would like to express its disappointment in relation to the disparaging comments made recently by Paolo Di Canio, regarding the club and its players.
"The club is immensely proud of its players for the dignified and restrained manner in which they have conducted themselves publicly since Mr Di Canio's departure and it is particularly disappointing to read such comments when there are legal obligations in place to ensure such behaviour does not occur.
"The club is now considering its position with its legal representatives.
"Having reached a cup final for the first time in 22 years, whilst also enjoying a run of only one loss in 12 games, we want to focus on what is a positive time for the football club and we would hope it is possible to draw a line under this matter quickly and that there will be no repetition.
"Neither the club, head coach Gus Poyet nor the players will be making any further comment on the situation.
"We are looking forward, not back and are focusing on the vital games we have ahead of us."