Di Canio, appointed as successor to the sacked Martin O'Neill in March, has been speaking publicly about what he sees as a lack of discipline among the players at the Wearside club, seven of whom he fined last week.
Defenders Phil Bardsley and Matt Kilgallon were dropped from the matchday squad for Sunday's Barclays Premier League clash at Tottenham after they were pictured celebrating on a night out in a casino earlier in the week, with the former lying on the floor covered in £50 notes.
In his post-match press conference at the weekend, Di Canio said: "I thought that at (his previous club) Swindon (there were) arrogant, ignorant footballers because they've not had many chances to stay at the top level.
"I have to tell you unfortunately I found a worse environment in terms of discipline in this club."
That was part of a lengthy rant about his players from Di Canio, who stressed the need for the matter to be addressed and also claimed the PFA "excuse people that behave like Phil Bardsley.(even though) the PFA don't pay them, it's a private club that pays them."
Taylor, without being drawn on specific names or details of the fines, on Tuesday confirmed that members of the Sunderland squad had been in touch with the PFA regarding former West Ham midfielder Di Canio, and emphasised that the union were examining the situation closely.
Taylor told Press Association Sport: "We know Paolo as a player and a manager, and he is a bit volatile.
"But he knows, from when he was a player with the PFA, what we are about. We represented him then, the same as we also represent the players (now).
"One point he made was about Sunderland being able to do what they want - well they can't. There is a disciplinary procedure that is agreed.
"We obviously agree with discipline, but that has to be in line with the Football Association and the Premier League. From that point of view, there is a due process.
"It is not going to help matters blasting players in public, but that is what he has done, so we will deal with it. It is not always conducive to good player-management relations.
"He is his own man, but they do have to abide by laid-down procedures and Sunderland, being a member of the Premier League, know that as well as anybody.
"We don't want to get into confrontation, but we have a job to do and we need the players to know that."
He added: "It is just a general involvement to make sure Sunderland are abiding by the laid-down procedures. If any player wishes to appeal then they have the right to do so.
"We are going through the paperwork and looking at the different individual circumstances.
"We did have a problem at Swindon that we needed to deal with as well, so this is not a total surprise."
Meanwhile, Sunderland winger Adam Johnson has made it clear he is in favour of Di Canio's hardline approach if it brings about an improvement in results.
Under Di Canio, the Black Cats took eight points from their final seven games this season and finished 17th in the table.
Johnson, quoted by the Northern Echo, said: "He's come in, and managers have new things that they want to do.
"The gaffer is big on discipline and if it means us getting more wins, I'm all for it.
"There's nothing worse than losing game after game after game after game all season. I haven't been used to that in my career, so it's been difficult.
"It's been poor, very poor, I think. The table doesn't lie. I think the only thing that we can say is that the only way is up for us now. We can't get any lower to be honest.
"We survived, and now next season all we can do is progress. That's the positive way of looking at it."