Sunderland's new manager has been repeatedly questioned about his political beliefs since he succeeded Martin O'Neill, and the Italian was last week forced to deny supporting "the ideology of fascism".
Di Canio takes his side to St James' Park this weekend for his first north-east derby and can expect a rough reception from the home crowd.
But local police chief superintendent Steve Neill has warned fans to keep their hostility within the law, saying: "Offensive behaviour can constitute a criminal offence and such behaviour is taken seriously.
"Offensive gestures, particularly those with a suggestion of racist connotations, are completely unacceptable and we will take positive action against anyone seen acting in an offensive or racist manner.
"While some individuals may see this sort of behaviour as a means of poking fun at opposing fans - it is not a joke.
"Football matches are routinely monitored by CCTV and even if action is not taken during the match, it can be checked retrospectively.
"We have demonstrated on numerous previous occasions our ability to trace offenders and put them before the courts, which can lead to a criminal record and possible football banning order.
"I would urge fans to act responsibly and reflect upon the impact any form of disorder or offensive behaviour has on others, themselves, the reputation of both clubs and the North East."